<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    Form 10-Q

[X]     Quarterly report pursuant to Section 13 or 15(d) of the Securities
        Exchange Act of 1934 for the quarterly period ended June 30, 1998

                                       or

[ ]     Transition report pursuant to Section 13 or 15(d) of the Securities
        Exchange Act of 1934 for the transition period from ________ to _______.

Commission file number 0-25560 

                                 CELERITEK, INC.
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

             California                                 77-0057484
    (State or other jurisdiction of                  (I.R.S. Employer
    incorporation or organization)                 Identification No.)

   3236 Scott Blvd., Santa Clara, CA                      95054
(Address of principal executive offices)                (Zip code)

                                 (408) 986-5060
--------------------------------------------------------------------------------
              (Registrant's telephone number, including area code)

                                 NOT APPLICABLE
--------------------------------------------------------------------------------
              (Former name, former address and former fiscal year,
                         if changed since last report)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days: [ X ] Yes [ ] No

Applicable only to corporate issuers:

Indicate the number of shares outstanding of each of the issuer's classes of
stock, as of the latest practicable date.

Common Stock, No Par Value:  7,214,027 shares as of July 26, 1998


<PAGE>   2
                                 CELERITEK, INC.


<TABLE>
<CAPTION>
PART I: FINANCIAL INFORMATION                                                        PAGE
                                                                                     ----
<S>                                                                                  <C>
         Item 1: Financial Statements (Unaudited)

               Condensed Consolidated Balance                                          1
               Sheets:  June 30, 1998 and March 31, 1998

               Condensed Consolidated Statements of Operations:                        2
               Three months ended June 30, 1998 and 1997

               Condensed Consolidated Statements of Cash Flows:                        3
               Three months ended June 30, 1998 and 1997

               Notes to Condensed Consolidated Financial Statements                    4


         Item 2: Management's Discussion and Analysis of Financial Condition
               and Results of Operations                                              6 - 10




PART II: OTHER INFORMATION



         Item 6: Exhibits and Reports on Form 8-K                                     11




SIGNATURES                                                                            12
</TABLE>


<PAGE>   3
CELERITEK, INC.
CONDENSED CONSOLIDATED BALANCE SHEETS
(In Thousands)


<TABLE>
<CAPTION>
                                                                   June 30,         March 31,
                                                                     1998             1998
                                                                 -------------    -------------
                                                                  (Unaudited)        (Note)
<S>                                                              <C>              <C>          
ASSETS
Current assets:
  Cash and cash equivalents                                      $       4,588    $       4,022
  Short-term investments                                                 7,000            7,500
  Accounts receivable, net                                              11,249           15,816
  Inventories                                                           10,673           10,635
  Prepaid expenses and other current assets                              2,515              415
  Deferred tax assets                                                    1,927            1,927
                                                                 -------------    -------------
           Total current assets                                         37,952           40,315
Property and equipment, net                                              8,207            8,042
Other assets                                                               124               91
                                                                 -------------    -------------
Total assets                                                     $      46,283    $      48,448
                                                                 =============    =============

LIABILITIES & SHAREHOLDERS' EQUITY 
Current liabilities:
  Current portion of long-term debt                              $         639    $         333
  Current obligations under capital leases                                  70               70
  Accounts payable                                                       4,919            4,491
  Accrued payroll                                                        2,306            1,570
  Accrued liabilities                                                    3,016            4,065
                                                                 -------------    -------------
          Total current liabilities                                     10,950           10,529
Long-term debt, less current portion                                     1,306              667
Non-current obligations under capital leases                               220              239
Shareholders' equity                                                    33,807           37,013
                                                                 -------------    -------------
Total liabilities and shareholders' equity                       $      46,283    $      48,448
                                                                 =============    =============
</TABLE>


Note: The balance sheet at March 31, 1998 has been derived from the audited
financial statements at that date but does not include all of the information
and footnotes required by generally accepted accounting principles for complete
financial statements.


                             See accompanying notes.


                                     Page 1


<PAGE>   4
CELERITEK, INC.
CONDENSED CONSOLIDATED STATEMENTS OF OPERATIONS
(In Thousands, Except Per Share Amounts)
(Unaudited)


<TABLE>
<CAPTION>
                                                            Three Months Ended
                                                                  June 30,
                                                      --------------------------------
                                                          1998              1997
                                                      -------------      -------------
<S>                                                   <C>                <C>          
Total net sales                                       $      10,196      $      12,595
Cost of goods sold                                           11,466              8,223
                                                      -------------      -------------

Gross profit (loss)                                          (1,270)             4,372
Operating expenses:
  Research and development                                    1,861              1,208
  Selling, general and  administrative                        2,502              1,795
                                                      -------------      -------------
Total operating expenses                                      4,363              3,003

Income (loss) from operations                                (5,633)             1,369
Interest income (expense) and other, net                         (6)               148
                                                      -------------      -------------

Income (loss) before income tax                              (5,639)             1,517
Provision (benefit) for income taxes                         (2,143)               561
                                                      -------------      -------------
Net income (loss)                                     $      (3,496)     $         956
                                                      =============      =============

Basic earnings (loss) per share                       $       (0.48)     $        0.13
                                                      =============      =============
Diluted earnings (loss) per share                     $       (0.48)     $        0.13
                                                      =============      =============

Weighted average common shares outstanding                    7,210              7,098
Common shares outstanding, assuming dilution                  7,210              7,366
</TABLE>


                             See accompanying notes.


                                     Page 2


<PAGE>   5
CELERITEK, INC.
CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS
(In Thousands)
(unaudited)


<TABLE>
<CAPTION>
                                                                                              Three Months Ended
                                                                                        -------------------------------
                                                                                           June 30,         June 30,
                                                                                            1998              1997
                                                                                        -------------     -------------
<S>                                                                                     <C>               <C>          
OPERATING ACTIVITIES
Net income (loss)                                                                       $      (3,496)    $         956
Adjustment to reconcile net income (loss) to
  net cash used in operating activities:
    Depreciation, amortization and other                                                          767               562
    Changes in operating assets and liabilities                                                 2,544            (1,692)
                                                                                        -------------     -------------
Net cash used in operating activities                                                            (185)             (174)

INVESTING ACTIVITIES
Purchase of property and equipment                                                               (932)           (1,390)
Decrease (increase) in other assets                                                               (33)              (48)
Purchases of short-term investments                                                                --            (4,330)
Sales of short-term investments                                                                   500             4,850
                                                                                        -------------     -------------
Net cash used in investing activities                                                            (465)             (918)

FINANCING ACTIVITIES
Payments on long-term debt                                                                        (55)               --
Borrowings on long-term debt                                                                    1,000                --
Payments on obligations under capital leases                                                      (19)               --
Proceeds from issuance of common stock                                                            290                29
                                                                                        -------------     -------------
Net cash provided by financing activities                                                       1,216                29

Increase (decrease) in cash and cash equivalents                                                  566            (1,063)
Cash and cash equivalents at beginning of period                                                4,022             7,033
                                                                                        -------------     -------------
Cash and cash equivalents at end of period                                              $       4,588     $       5,970
                                                                                        =============     =============

Supplemental disclosures of cash flow information: 
Cash paid during the period for:                                                            
     Income taxes                                                                       $         975     $       1,048
     Interest                                                                                      73                --
</TABLE>


                            See accompanying notes.


                                     Page 3


<PAGE>   6
CELERITEK, INC.

Notes to Condensed Consolidated Financial Statements

(Unaudited)

June 30, 1998

1.      BASIS OF PRESENTATION

        The accompanying unaudited condensed consolidated financial statements
        have been prepared in accordance with generally accepted accounting
        principles for interim financial information and with the instructions
        to Form 10-Q and Article 10 of Regulation S-X. Accordingly, they do not
        include all of the information and footnotes required by generally
        accepted accounting principles for complete financial statements. In the
        opinion of management, all adjustments (consisting of normal recurring
        accruals) considered necessary for a fair presentation have been
        included. Operating results for the three-month period ended June 30,
        1998 are not necessarily indicative of the results that may be expected
        for the year ended March 31, 1999. This financial information should be
        read in conjunction with the consolidated financial statements and notes
        thereto included in the Company's annual report on Form 10-K for the
        year ended March 31, 1998.

2.      INVENTORIES

        The components of inventory consist of the following:


<TABLE>
<CAPTION>
                           June 30,          March 31,
                             1998              1998
                         -------------    -------------
                                (In Thousands)
<S>                      <C>              <C>          
Raw materials            $       3,099    $       3,405
Work-in-process                  7,574            7,230
                         -------------    -------------
                         $      10,673    $      10,635
                         =============    =============
</TABLE>


3.      LINES OF CREDIT

        On September 12, 1997, the Company extended and amended two revolving
        lines of credit. The first line of credit for $4,000,000 will expire on
        September 11, 1998 and will bear interest at the bank's reference rate
        (8.5% at June 30, 1998). The second line of credit is for $1,000,000 and
        will also expire on September 11, 1998. On March 11, 1998 and September
        11, 1998, any outstanding balance on the second line of credit will be
        converted to a term loan of thirty-six months. Borrowings under the
        second line of credit and term loan will bear interest at the bank's
        reference rate plus 0.5%. On May 29, 1998, the Company amended the
        second line of credit to provide borrowings of up to $1,944,444. As of
        June 30, 


                                     Page 4


<PAGE>   7
        1998, the Company had borrowings totaling $1,944,444 under the second
        line of credit, of which $944,444 is outstanding as a term loan of
        thirty-six months and no borrowings under the first line of credit. The
        loan agreement contains certain covenants, including among others,
        covenants to maintain certain financial ratios, profitability levels, a
        minimum tangible net worth of $33,000,000, and limits the payment of
        dividends. As of the June 30, 1998, the Company was not meeting its debt
        service ratio and profitability covenants. At this time, the Company
        does not believe, based on discussions with its bank, that it is likely
        that the loan agreement will be terminated. The Company's business,
        operating results and financial condition would be materially adversely
        affected if the loan agreement were to be terminated.

4.      EARNINGS PER SHARE

        In accordance with the Statement of Financial Accounting Standard No.
        128, "Earnings per Share," basic earnings (loss) per common share is
        computed using the weighted average common shares outstanding during the
        period. Diluted earnings per common share incorporates the incremental
        shares issuable upon the assumed exercise of stock options when diluted.

        The following table sets forth the computation of basic and diluted
        earnings (loss) per share (in thousands, except per share data):


<TABLE>
<CAPTION>
                                                         Three months ended
                                                             June 30,
                                                ------------------------------------
BASIC                                               1998                   1997
                                                -------------          -------------
<S>                                             <C>                    <C>          
Net income (loss)                               $      (3,496)         $         956
                                                =============          =============

Weighted common shares outstanding                      7,210                  7,098
                                                =============          =============
Basic earnings (loss) per common share          $       (0.48)         $        0.13
                                                =============          =============


DILUTED

Net income                                      $      (3,496)         $         956
                                                =============          =============

Weighted common shares outstanding                      7,210                  7,098
Dilutive effect of stock options                           --                    268
                                                -------------          -------------
Weighted common shares outstanding,
  assuming dilution                                     7,210                  7,366
                                                =============          =============
Diluted earnings per common share               $       (0.48)         $        0.13
                                                =============          =============
</TABLE>


                                     Page 5


<PAGE>   8
MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS OF
OPERATIONS


        This Quarterly Report on Form 10-Q contains forward-looking statements
within the meaning of Section 27A of the Securities Act of 1933 and Section 21E
of the Securities Exchange Act of 1934. These forward-looking statements
represent the Company's expectations or beliefs concerning future events and
include statements, among others, regarding length and timing of delays and the
long-term potential of the market. Actual results could differ materially from
those projected in the forward-looking statements as a result of the risk
factors set forth below under "Risks, Trends, and Uncertainties."


RESULT OF OPERATIONS - FIRST QUARTER OF FISCAL 1998 COMPARED TO FIRST QUARTER OF
FISCAL 1999: 

        Total net sales decreased 19% from $12.6 million for the first quarter
of fiscal 1998 to $10.2 million for the first quarter of fiscal 1999. Total net
sales to commercial customers decreased 17% from $6.4 million for the first
quarter of fiscal 1998 to $5.3 million for the first quarter of fiscal 1999,
primarily as a result of delayed contracts by several subsystem customers. The
Company expects the subsytems market, particularly the microwave radio segment,
to remain sluggish at least through the second quarter of fiscal 1999. Total net
sales to defense customers decreased by 21% from $6.2 million in the first
quarter of fiscal 1998 to $4.9 million for the first quarter of fiscal 1999,
primarily due to customer delays in product qualifications on two programs. See
"Risks, Trends, and Uncertainties - Potential Fluctuations in Quarterly
Results."

        Gross margin decreased from 35% of net sales in the first quarter of
fiscal 1998 to a loss of 12% of net sales in the first quarter of fiscal 1999.
The decrease in gross margin was primarily due to an inventory write down of
$3.1 million related to delayed or canceled contracts and to a lesser extent,
increased manufacturing overhead to support an anticipated increase in sales
volume.

        Research and development expenses increased 54% from $1.2 million, or
10% of net sales, in the first quarter of fiscal 1998 to $1.9 million, or 18% of
net sales, in the first quarter of fiscal 1999 reflecting the Company's
continuing investment in commercial product development. The increase was
primarily due to an increase in head count and related expenses. See "Risks,
Trends, and Uncertainties - Dependence on Key Personnel."

        Selling, general and administrative expenses increased from $1.8
million, or 14% of net sales, in the first quarter of fiscal 1998 to $2.5
million, or 25% of net sales, in the first quarter of fiscal 1999. The increase
was primarily due to increased head count and bad debt expense.

        Interest income (expense) and other, net decreased 104% from $148,000 of
interest income in the first quarter of fiscal 1998 to $6,000 of interest
expense in the first quarter of fiscal 1999. The decreased was primarily due to
lower average cash balances as a result of cash being used for 


                                     Page 6


<PAGE>   9
working capital and, to a lesser extent, capital expenditures in connection with
activities directed at increasing capacity. The increased interest expense was
due to equipment purchases financed through long-term debt and capital leases.


LIQUIDITY AND CAPITAL RESOURCES

        The Company has funded its operations to date primarily through cash
flows from operations and sales of equity securities including the initial
public offering of common stock completed in December 1995 and January 1996,
which generated net proceeds of approximately $12.1 million.

        During the quarter ended June 30, 1998, the Company used cash for
working capital and capital expenditures and financed $1.0 million of equipment
purchases through long-term debt.

        The Company has two revolving lines of credit. The first line of credit
for $4,000,000 will expire on September 11, 1998 and will bear interest at the
bank's reference rate (8.5% at June 30, 1998). The second line of credit is for
$1,944,444 and will also expire on September 11, 1998. On March 11, 1998 and
September 11, 1998, any outstanding balance on the second line of credit will be
converted to a term loan of thirty-six months. Borrowings under the second line
of credit and term loan will bear interest at the bank's reference rate plus
0.5%. The Company's loan agreement contains certain covenants, including among
others, covenants to maintain certain financial ratios, profitability levels, a
minimum tangible net worth of $33,000,000, and limits the payment of dividends.
As of the June 30, 1998, the Company was not meeting its debt service ratio and
profitability covenants. At this time, the Company does not believe, based on
discussions with its bank, that it is likely that the loan agreement will be
terminated. The Company's business, operating results and financial condition
would be materially adversely affected if the loan agreement were to be
terminated.

        As of June 30, 1998, the Company had $4.6 million of cash and cash
equivalents, $7.0 million of short-term investments and $27.0 million of working
capital. The Company believes that the current capital resources combined with
cash generated from operations and borrowings available from its lines of credit
will be sufficient to meet its liquidity and capital expenditure requirements at
least through fiscal 1999.




RISKS, TRENDS, AND UNCERTAINTIES

The following risk factors should be carefully reviewed in addition to the other
information contained in this Quarterly Report in Form 10-Q.


        Potential Fluctuations in Quarterly Results. The Company's quarterly
results have fluctuated in the past, and may continue to fluctuate in the
future, due to a number of 


                                     Page 7


<PAGE>   10
factors, including: the timing, cancellation or delay of customer orders; the
mix of products sold; changes in manufacturing capacity and variations in the
utilization of this capacity; the timing of new product introductions by the
Company or its competitors; the long sales cycle associated with the Company's
application-specific products; market acceptance of the Company's and its
customers' products; variations in average selling prices of semiconductors;
variations in manufacturing yields; changes in inventory levels and other
competitive factors. Any unfavorable changes in the factors listed above or
others could have a material adverse effect on the Company's business, operating
results and financial condition. For example, in the first quarter of fiscal
1999, a number of contracts were either terminated or delayed by both commercial
and defense customers. There can be no assurance that additional contracts will
not be cancelled of delayed or that customers will ever reinstate orders under
contracts which have been delayed. There can be no assurance that the Company
will be able to maintain quarterly profitability in the future. See "Risks,
Trends, and Uncertainties - Dependence on Limited Number of OEM Customers."

        Continued Penetration of Commercial Markets; New Product Introductions.
The Company's ability to grow will depend substantially on its ability to
continue to apply its radio frequency ("RF") and microwave signal processing
expertise and GaAs semiconductor technologies to existing and emerging
commercial wireless communications markets. If the Company is unable to design,
manufacture and market new products for existing or emerging commercial markets
successfully, its business, operating results and financial condition will be
materially adversely affected. Furthermore, if the markets for the Company's
products in the commercial wireless communications area fail to grow, or grow
more slowly than anticipated, the Company's business, operating results and
financial condition could be materially adversely affected.

        Yields and the High Degree of Fixed Costs in the Manufacturing
Operation. The Company has in the past and may in the future experience
significant delays in product shipments due to lower than expected production
yields, and there can be no assurance that the Company will not experience
problems in maintaining acceptable yields in the future. The Company's
manufacturing yields vary significantly among products, depending on a given
product's complexity and the Company's experience in manufacturing the product.
To the extent that the Company does not maintain acceptable yields, its
business, operating results, and financial condition could be materially
adversely affected. In addition, the Company's fixed costs, which consist
primarily of investments in manufacturing equipment, repair, maintenance, and
depreciation costs of such equipment and fixed labor costs related to
manufacturing and process engineering, are high and during periods of decreased
demand, the high fixed costs could have a material adverse effect on the
Company's business, operating results, and financial condition.

        In addition, the Company has completed its new facility to house its
wireless subsystems manufacturing operations and has begun manufacturing
operations in the new facility during the third quarter of fiscal 1998. Even
though the Company has increased overall capacity, there can be no assurance
that the Company will be successful in its efforts to generate orders to utilize
the additional capacity, or that net sales and gross margin will increase.


                                     Page 8


<PAGE>   11
        Dependence on a Limited Number of OEM Customers. A relatively limited
number of OEM customers historically have accounted for a substantial portion of
the Company's sales. In fiscal 1998 and the three months ended June 30, 1998,
sales to the Company's top ten customers accounted for approximately 63% and 73%
of total net sales, respectively. In the three months ended June 30, 1998, Arrow
Electronics, P-Com and Sippican Inc., each, accounted for approximately 12% of
total net sales. The Company expects that sales of its products to a limited
number of OEM customers will continue to account for a high percentage of its
sales for the foreseeable future, although sales to any single customer are
subject to significant variability from quarter to quarter. Such fluctuations or
a complete loss of one or more of these customers, could have a material adverse
effect on the Company's business, operating results and financial condition.

        No Assurance of Product Performance and Reliability. The Company's
customers establish demanding specifications for performance and reliability.
There can be no assurance that problems will not occur in the future with
respect to performance and reliability of the Company's products. If such
problems occur, the Company could experience increased costs, delays in or
reductions, cancellations or rescheduling of orders and shipments, product
returns and discounts, and product redesigns, any of which would have a material
adverse effect on the Company's business, operating results and financial
condition.

        Rapid Technological Change. The markets in which the Company competes
are characterized by rapidly changing technologies, evolving industry standards
and continuous improvements in products and services. There can be no assurance
that the Company will be able to respond to technological advances, changes in
customer requirements or changes in regulatory requirements or industry
standards, and any significant delays in the development, introduction or
shipment of products could have a material adverse effect on the Company's
business, operating results and financial condition.

        Competition. The markets in which the Company competes are intensely
competitive and the Company expects competition to increase. Most of the
Company's current and potential competitors have significantly greater
financial, technical, manufacturing and marketing resources than the Company and
have achieved market acceptance of their existing technologies. The ability of
the Company to compete successfully depends upon a number of factors, including
the rate at which customers incorporate the Company's products into their
systems, product quality and performance, price, experienced sales and marketing
personnel, rapid development of new products and features, evolving industry
standards and the number and nature of the Company's competitors. There can be
no assurance that the Company will be able to compete successfully in the
future, which would have a material adverse effect on the Company's business,
operating results and financial condition.

        Dependence on Key Suppliers. Certain components used by the Company in
its existing products are only available from single sources, and certain other
components are presently available or acquired only from a limited number of
suppliers. In the event that its single source suppliers are unable to fulfill
the Company's requirements in a timely 


                                     Page 9


<PAGE>   12
manner, the Company may experience an interruption in production until
alternative sources of supply can be obtained, which could damage customer
relationships or have a material adverse effect on the Company's business,
operating results and financial condition.

        In addition, the Company contracts with a third party vendor in Asia to
assemble certain of its subsystem division components to reduce manufacturing
labor costs. Additionally, the Company contracts with several third party
vendors in Asia to assemble its GaAs chips into integrated circuit packages.
Although the Company strives to maintain more than one vendor for each assembly
process, it is not always possible due to volume and quality issues. To the
extent that any of the assembly vendors are not able to provide a sufficient
level of service with an acceptable quality level, the Company could have
difficulty meeting its delivery commitments which could materially adversely
impact the Company's financial, operating and financial results

        Dependence on Key Personnel. The Company's future success depends in
significant part upon the continued service of its key technical and senior
management personnel and its continuing ability to attract and retain highly
qualified technical and managerial personnel. In particular, the Company in the
past has experienced difficulty attracting and retaining qualified engineers and
thin-film microwave technicians. Competition for these kinds of experienced
personnel is intense, and there can be no assurance that the Company can retain
its key technical and managerial employees or that it can attract, assimilate or
retain other highly qualified technical and managerial personnel in the future.
The failure to attract, assimilate or retain key personnel could have a material
adverse effect on the Company's business, operating results and financial
condition.


                                    Page 10


<PAGE>   13
Item 6.        Exhibits and Reports on Form 8-K


The following exhibit is included herein:

        Exhibit 10.14 Loan modification agreement dated May 29, 1998
                      between Registrant and Silicon Valley Bank.


Report on Form 8-K during the three months ended June 30, 1998.

        Form 8-K filed on May 7, 1998.
                       Disclosure of effect of adoption of FAS 128.


                                    Page 11


<PAGE>   14
SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                      Celeritek, Inc.
                                      (Registrant)



Date:   August 14, 1998               /s/ MARGARET E. SMITH
                                      ---------------------------
                                      Margaret E. Smith, Vice President,
                                      Chief Financial Officer and Assistant
                                      Secretary


                                    Page 12


<PAGE>   15
                               INDEX TO EXHIBITS


<TABLE>
<CAPTION>
EXHIBIT 
NUMBER                        DESCRIPTION
------                        -----------
<S>            <C>                    
10.14          Loan modification agreement dated May 29, 1998 between Registrant
               and Silicon Valley Bank.

27             Financial Data Schedule
</TABLE>