<PAGE>   1


================================================================================

                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

                           -------------------------

                                    FORM 10-Q
(MARK ONE)
            [X]  QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                FOR THE QUARTERLY PERIOD ENDED DECEMBER 31, 1999

                                       OR

            [ ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                          COMMISSION FILE NUMBER 1-9965



                           KEITHLEY INSTRUMENTS, INC.
             (Exact name of registrant as specified in its charter)

                      OHIO                              34-0794417
         (State or other jurisdiction of             (I.R.S. Employer
         incorporation or organization)              Identification No.)

                      28775 AURORA ROAD, SOLON, OHIO 44139
               (Address of principal executive offices) (Zip Code)

       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (440) 248-0400


         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.

                                   YES  X  NO
                                       ---    ---

         As of February 1, 2000 there were outstanding 4,464,796 Common Shares,
without par value, and 2,692,028 Class B Common Shares, without par value.

================================================================================


<PAGE>   2



                         PART I. FINANCIAL INFORMATION
                         -----------------------------

ITEM 1.  Financial Statements.
------   ---------------------

                           KEITHLEY INSTRUMENTS, INC.
                           Consolidated Balance Sheet
                            (In Thousands of Dollars)
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                            DECEMBER 31,                  SEPTEMBER 30,
                                                                            ------------                  -------------
                                                                       1999              1998                  1999
                                                                       ----              ----                  ----
<S>                                                                  <C>               <C>                   <C>
Assets

Current assets:
     Cash and cash equivalents                                       $ 13,097          $ 16,961              $ 13,426
     Accounts receivable and other, net                                17,646            13,785                19,633
     Inventories:
           Raw materials                                                7,439             5,175                 4,853
           Work in process                                              3,389             2,667                 4,009
           Finished products                                            2,291             1,875                 2,187
                                                                      -------           -------               -------
             Total inventories                                         13,119             9,717                11,049
     Other current assets                                               3,811             3,873                 3,593
                                                                      -------           -------               -------
             Total current assets                                      47,673            44,336                47,701
                                                                       ------            ------                ------

Property, plant and equipment, at cost                                 38,193            39,211                38,293
Less-Accumulated depreciation                                          25,815            25,526                25,617
                                                                       ------            ------                ------
Net property, plant and equipment                                      12,378            13,685                12,676
                                                                       ------            ------                ------

Other assets                                                           14,531            14,045                14,374
                                                                       ------            ------                ------
Total assets                                                          $74,582           $72,066               $74,751
                                                                       ======            ======                ======


Liabilities and Shareholders' Equity
------------------------------------

Current liabilities:
     Short-term debt and current
       installments on long-term debt                               $     515          $     --             $      --
     Accounts payable                                                   8,217             6,207                 8,119
     Accrued payroll and related expenses                               3,866             4,490                 5,872
     Other accrued expenses                                             5,988             6,606                 6,046
     Income taxes payable                                               3,709             4,965                 3,382
                                                                       ------            ------                ------
           Total current liabilities                                   22,295            22,268                23,419
                                                                       ------            ------                ------

Long-term debt                                                          3,000             6,599                 3,000
Other long-term liabilities                                             4,951             4,198                 4,551

Shareholders' equity:
     Paid-in-capital                                                    9,127             9,106                 9,270
     Earnings reinvested in the business                               45,866            33,418                42,623
     Accumulated other comprehensive income                              (175)              375                   112
     Unamortized portion of restricted stock                             (228)             (272)                 (239)
     Common shares held in treasury, at cost                          (10,254)           (3,626)               (7,985)
                                                                       ------           -------               -------
           Total shareholders' equity                                  44,336            39,001                43,781
                                                                       ------            ------                ------
Total liabilities and shareholders' equity                            $74,582           $72,066               $74,751
                                                                       ======            ======                ======
</TABLE>




                                       2
<PAGE>   3



                           KEITHLEY INSTRUMENTS, INC.
                        Consolidated Statement of Income
               (In Thousands of Dollars Except for Per Share Data)
                                   (Unaudited)



<TABLE>
<CAPTION>
                                                         FOR THE THREE MONTHS
                                                           ENDED DECEMBER 31,
                                                        1999               1998
                                                        ----               ----


<S>                                                   <C>                <C>
Net sales                                             $ 29,760           $ 20,881

Cost of goods sold                                      11,760              8,806

Selling, general and administrative expenses            10,339              8,868

Product development expenses                             2,828              2,282

Gain on sale of business                                  (477)            (4,808)

Net financing income                                       (90)               (39)
                                                      --------           --------

Income before income taxes                               5,400              5,772

Income taxes                                             1,890              1,989
                                                      --------           --------

Net income                                            $  3,510           $  3,783
                                                      ========           ========


Basic earnings per share                              $    .49           $    .49
                                                      ========           ========

Diluted earnings per share                            $    .46           $    .48
                                                      ========           ========

Cash dividends per Common Share                       $   .041           $   .033
                                                      ========           ========

Cash dividends per Class B
Common Share                                          $   .033           $   .026
                                                      ========           ========
</TABLE>



                                       3
<PAGE>   4



                           KEITHLEY INSTRUMENTS, INC.
                      Consolidated Statement of Cash Flows
                            (In Thousands of Dollars)
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                     FOR THE THREE MONTHS
                                                                      ENDED DECEMBER 31,
                                                                    1999               1998
                                                                    ----               ----
<S>                                                               <C>                <C>
Cash flows from operating activities:
     Net income                                                   $  3,510           $  3,783
     Expenses not requiring outlay of cash                             832                735
     Gain on sale of business                                         (477)            (4,808)
     Changes in working capital                                     (1,579)             2,857
     Other operating activities                                        180                (47)
                                                                  --------           --------
     Net cash provided by operating activities                       2,466              2,520
                                                                  --------           --------

Cash flows from investing activities:
     Payments for property, plant, and equipment                      (546)              (284)
     Sale of assets - net                                               --              8,393
     Other investing activities-net                                     37                  6
                                                                  --------           --------
     Net cash provided by (used in) investing activities              (509)             8,115
                                                                  --------           --------

Cash flows from financing activities:
     Increase in short-term debt                                       515                 --
     Borrowing of long-term debt                                        --                500
     Cash dividends                                                   (267)              (235)
     Repurchase of treasury stock                                   (3,013)            (3,246)
     Other transactions-net                                            602                 --
                                                                  --------           --------
     Net cash used in financing activities                          (2,163)            (2,981)
                                                                  --------           --------

Effect of changes in foreign currency exchange rates                  (123)               (14)
                                                                  --------           --------

Increase (decrease) in cash and cash equivalents                      (329)             7,640
Cash and cash equivalents at beginning of period                    13,426              9,321
                                                                  --------           --------
Cash and cash equivalents at end of period                        $ 13,097           $ 16,961
                                                                  ========           ========

Supplemental disclosures of cash flow information
-------------------------------------------------
     Cash paid during the period for:
           Income taxes                                           $    730           $  1,591
           Interest                                                      7                 45
</TABLE>

Disclosure of accounting policy
-------------------------------

     For purposes of this statement, the Company considers all highly liquid
investments with maturities of three months or less when purchased to be cash
equivalents.


                                       4
<PAGE>   5



                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                   ------------------------------------------
                (In thousands of dollars, except for share data)
                ------------------------------------------------


A.   Management Representation
     -------------------------

     The consolidated financial statements at December 31, 1999 and 1998, and
     for the three month periods then ended have not been examined by
     independents accountants, but in the opinion of the management of Keithley
     Instruments, Inc., all adjustments necessary to a fair statement of the
     consolidated balance sheet, consolidated statement of income and
     consolidated statement of cash flows for those periods have been included.
     All adjustments included are of a normal recurring nature.

B.   Earnings per share denominator
     ------------------------------

     The weighted average number of shares and share equivalents used in
     determining basic earnings per share and diluted earnings per share was
     7,094,289 and 7,645,729 for the quarter ended December 31, 1999,
     respectively, and 7,780,105 and 7,876,240 for the quarter ended December
     31, 1998, respectively. Both Common Shares and Class B Common Shares are
     included in calculating the weighted average number of shares outstanding.

C.   Sale of assets
     --------------

     On November 9, 1998, the company sold certain assets used in the operation
     of its Quantox product line to KLA-Tencor Corporation for $9,147 in cash.
     The agreement, which was effective October 31, 1998, included the sale of
     the Quantox inventory, certain machinery, equipment and other tangible
     personal property. The company retained the accounts receivable. The sale
     resulted in a pretax gain of $4,808, or $0.39 per share after taxes,
     recorded in the first quarter of fiscal 1999. Additional pretax gains of
     $345, or $0.03 per share after taxes, and of $477 pretax, or $0.04 per
     share after taxes, were recorded in the fourth quarter of fiscal 1999 and
     the first quarter of fiscal 2000, respectively, for businesses previously
     sold. At the time of the sales of these businesses, the company established
     liabilities for certain items that were to be settled at future dates. The
     additional adjustments represent the settlement of certain of these issues.

D.   Dutch Auction and stock repurchase program
     ------------------------------------------

     On November 11, 1998, the company commenced a tender offer to repurchase up
     to 2,000,000 of its Common Shares, or approximately 25 percent of the
     outstanding Common Shares and Class B Common Shares combined. The offer was
     conducted through a procedure commonly known as a "Dutch Auction" in which
     shareholders could tender their shares at prices not in excess of $7.00 nor
     less than $5.75 per share. The offer expired on December 10, 1998, and
     resulted in the repurchase of 405,733 Common Shares at $7.00 per share plus
     expenses of approximately $1.00 per share. At the conclusion of the Dutch
     Auction, the company's Board of Directors approved a program to repurchase
     up to 1,000,000 Common Shares, or approximately 13 percent of the
     outstanding Common Shares and Class B Common Shares combined, over a
     two-year period. The shares repurchased under both the Dutch Auction and
     the stock repurchase program will initially be held as treasury stock, and
     from time to time, may be reissued in settlement of stock options and the
     company's employee stock purchase plan. During the first quarter of fiscal
     2000 the Company repurchased 152,400 Common Shares at an average cost of
     $19.77 per share



                                       5
<PAGE>   6


     including commissions. The company has repurchased a total of 1,095,203
     Common Shares or approximately 14 percent of the combined Common and Class
     B Common Shares outstanding since the start of repurchase programs, at an
     average cost of $10.39 per share including commissions. The program, as
     authorized by the company's Board of Directors, allows for the repurchase
     of an additional 310,530 shares through December 2000. During the first
     quarter of fiscal 2000, the company reissued 91,096 shares (191,523 total
     since the start of the repurchase program) in settlement of shares
     purchased through the company's employee stock option and employee stock
     purchase plans.

E.   Comprehensive income
     --------------------

     On October 1, 1998, the company adopted Statement of Financial Accounting
     Standards No. 130, "Reporting Comprehensive Income" (SFAS 130), which
     establishes rules for reporting comprehensive income and its components.
     The adoption of SFAS 130 did not impact the company's net income or total
     shareholders' equity. Comprehensive income for the three months ended
     December 31, 1999 and 1998 is as follows:

<TABLE>
<CAPTION>
                                                                    December 31,
                                                               1999              1998
                                                              ------            ------

<S>                                                           <C>               <C>
                Net income                                    $3,510            $3,783
                Foreign currency translation
                  adjustments                                   (288)              (54)
                                                              ------            ------

                Comprehensive income                          $3,222            $3,729
                                                              ======            ======
</TABLE>



                                       6
<PAGE>   7


Item 2.  Management's Discussion and Analysis of Financial Condition and Results
-------  -----------------------------------------------------------------------
of Operations.
--------------

                            (In Thousands of Dollars)


Results of Operations
---------------------

First Quarter Fiscal 2000 Compared with First Quarter Fiscal 1999
-----------------------------------------------------------------

Net income for the first quarter of fiscal 2000 before a $0.04 per share gain on
the sale of a previously disposed business was $3,207 or $0.42 per share,
compared with $693, or $0.09 per share, in last year's quarter on a comparable
basis. Net income as reported for the first quarter of fiscal 2000 was $3,510,
or $0.46 per share, compared to $3,783, or $0.48 per share, in last year's
quarter which includes a gain of $0.39 per share for the sale of a business.
(See Note C.)

Net sales of $29,760 increased 43 percent from $20,881 in the prior year's first
quarter. Excluding sales from the Quantox product line (Quantox) sold in the
first quarter of fiscal 1999, net sales increased 47 percent. This was
principally due to strong sales for the company's products serving the
semiconductor and telecommunications industries. Geographically, sales from the
company's current businesses increased in all major geographies. Orders for the
first quarter of $37,735 increased 61 percent from the prior year's orders of
$23,377, excluding Quantox in last year's quarter, and were a new record high.
Several large orders from key customers caused otherwise strong orders to become
record orders. These customers ordered in larger quantities and at accelerated
levels from what they had previously indicated. Orders were particularly strong
for the company's products serving the semiconductor, telecommunications and
optoelectronics industries. Order backlog of $24,659 at December 31, 1999, grew
$5,318 during the quarter and was also a new record high.

Cost of goods sold as a percentage of net sales decreased to 39.5 percent from
42.2 percent in the prior year's first quarter. This was mainly due to improved
manufacturing efficiencies resulting from higher sales volume. The effect of
foreign exchange hedging on cost of goods sold was immaterial in both periods.

Selling, general and administrative expenses increased $1,471, or 17 percent,
from the prior year's quarter, but decreased as a percentage of net sales to
34.8 from 42.5 due to higher sales volume. The increase in dollars is due to new
marketing initiatives related to the internet and new products, as well as
increased employee incentive expenses due to higher earnings.

Product development expenses for the quarter of $2,828, or 9.5 percent of net
sales, increased from $2,282, or 10.9 percent of net sales, last year. The
increase is primarily due to development costs for new products including the
Model 2700 Multimeter/Data Acquisition System, PCI Data Acquisition boards and
new DriverLINX software.

On November 9, 1998, the company sold certain assets used in the operation of
its Quantox product line to KLA-Tencor Corporation. The sale was effective
October 31, 1998, and resulted in a gain of $4,808 pretax, or $0.39 per share
after taxes, recorded in the first quarter of fiscal 1999. During the first
quarter of fiscal 2000, an additional pretax gain of $477, or $0.04 per


                                       7
<PAGE>   8


share after taxes, was recorded for the sale. At the time of the sale of this
business, the company established liabilities for certain items that were to be
settled at future dates. The additional adjustment recorded in the first quarter
of fiscal 2000 represents the settlement of certain of these issues. (See Note
C.)

The company generated net financing income during the quarter of $90 versus $39
in the prior year. Lower average debt levels this year, resulting in lower
interest expense, combined with better rates on income earned on cash and cash
equivalents accounted for the improvement.

The effective tax rate for the quarter was 35.0 percent versus 34.5 percent last
year. The tax rate in the prior year's quarter on earnings excluding the gain on
the sale of a business was 28.1 percent. The tax rate in the 2000 quarter is
higher than the 1999 quarter due to higher earnings on normal operations and the
utilization of tax credits in the prior year, which are not available in the
current year.


Liquidity and Capital Resources
-------------------------------

During the first quarter, net cash provided by operations was $2,466. The
company used available cash of $3,013 to repurchase 152,400 Common Shares
through the stock repurchase program. (See Note D.) Additionally, the company
purchased $546 of capital equipment during the quarter. Total cash and cash
equivalents decreased $329 during the quarter to $13,097 at December 31, 1999.
Total debt of $3,515 at December 31, 1999, increased $515 during the quarter,
and the total debt-to-capital ratio was 7.3 percent at December 31, 1999.

The company expects to finance debt service, capital spending, the stock
repurchase program and working capital requirements through cash on hand and
cash provided by operations. At December 31, 1999, the company had available
unused lines of credit with domestic and foreign banks aggregating $26,610 of
which $4,610 were short-term and $22,000 were long-term.


Year 2000
---------

The company did not experience any significant disruptions or errors in its
operating or business systems when the date changed from 1999 to 2000. Based on
operations since January 1, 2000, the company does not expect any significant
impact to its on-going business as a result of the "Year 2000 issue." The
company could still be negatively impacted if its customers or suppliers are
adversely affected by the Year 2000 issue, however, the company is not aware of
any significant Year 2000 problems that have arisen for its customers or
suppliers.



                                       8
<PAGE>   9


Outlook
-------

Due to the record backlog level along with current business activity in the
semiconductor, telecommunications and optoelectronics industries, management
believes that the second quarter fiscal 2000 sales and operating earnings should
be better than those of the first quarter. However, quarter-to-quarter results
are always order dependent and the company's success is dependent upon continued
investment from customers in these key electronics industries.


Factors That May Affect Future Results
--------------------------------------

Information included above in the Outlook section of Management's Discussion and
Analysis of Financial Condition and Results of Operations relating to
expectations as to the company's sales and earnings for the second quarter,
constitute "forward-looking" statements, as that term is defined in the Private
Securities Litigation Reform Act of 1995. Such statements are subject to certain
risks and uncertainties that could cause actual results to differ materially
from those projected. Some of the factors that may affect future results are
discussed below.

Although the company operates in a single industry segment, certain of its
products and product lines are sold into the semiconductor industry. Growth in
demand for semiconductors, new technology and pricing drive the demand for new
semiconductor capital equipment. Historically, sales and order levels for this
business have been volatile which can affect revenue and earnings for the
company.

The company's business relies on the development of new high technology products
and services to provide solutions to customers' complex measurement needs. This
requires anticipation of customers' changing needs and emerging technology
trends. The company must make long-term investments and commit significant
resources before knowing whether its expectations will eventually result in
products that achieve market acceptance. The company incurs significant expenses
developing new products that may or may not result in significant sources of
revenue and earnings in the future.

In many cases the company's products compete directly with those offered by
other manufacturers. If any of the company's competitors were to develop
products or services that are more cost-effective or technically superior,
demand for the company's product offerings could slow.

The company's cost structure is comprised of costs that are directly related to
the level of sales, as well as costs that are fixed and do not fluctuate based
on quarterly sales levels. The company's ability to maintain its cost structure
or to further improve its cost structure depends on its ability to control those
costs that are fixed or semi-variable.

The company pays taxes in several jurisdictions throughout the world. The
company utilizes available tax credits and other tax planning strategies in an
effort to minimize the company's overall tax liability. The company's actual tax
rate for fiscal 2000 could change from what is currently anticipated due to
changes in various country's tax laws or changes in the company's overall tax
planning strategy.



                                       9
<PAGE>   10


The company currently has ten subsidiaries or sales offices located outside the
United States, and non-U.S. sales made up 43 percent of the company's revenue in
the first quarter of fiscal 2000. The company's future results could be
adversely affected by several factors, including changes in foreign currency
exchange rates, changes in a country's or region's political or economic
conditions, trade protection measures, import or export licensing requirements,
unexpected changes in regulatory requirements and natural disasters.

The company has modified its systems to accommodate the Euro. The cost of these
modifications was immaterial to the company's results of operations. Although
difficult to predict, any competitive implications and any impact on existing
financial instruments are expected to be immaterial to the company's results of
operations, financial condition or cash flows of future periods.




                                       10
<PAGE>   11

PART II.   OTHER INFORMATION
--------   -----------------


Item 6.  Exhibits and Reports on Form 8-K.
         ---------------------------------


           (a)  EXHIBITS.  The following exhibits are filed herewith:

           Exhibit
           Number          Exhibit
           ------          -------
           11    Statement Re Computation of Per Share Earnings

           27    Financial Data Schedule (EDGAR version only)


          (b)  REPORTS ON FORM 8-K. No reports on Form 8-K were filed during the
               quarterly period ended December 31, 1999.


                                   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.


                                    KEITHLEY INSTRUMENTS, INC.
                                    (Registrant)






Date:  February 11, 2000              /s/  Joseph P. Keithley
                                    --------------------------------------------
                                    Joseph P. Keithley
                                    Chairman, President and Chief Executive
                                    Officer
                                    (Principal Executive Officer)






Date:  February 11, 2000              /s/  Mark J. Plush
                                    --------------------------------------------
                                    Mark J. Plush
                                    Vice President and Chief Financial Officer
                                    (Principal Financial and Accounting Officer)


                                       11