<PAGE>
 

               UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             Washington, DC 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 October 31, 1998

[_]  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 0-5286


                        KEWAUNEE SCIENTIFIC CORPORATION
                        -------------------------------
            (Exact name of registrant as specified in its charter)

           Delaware                                              38-0715562
-------------------------------                                  ----------
(State or other jurisdiction of                               (I.R.S. Employer
incorporation or organization)                               Identification No.)

2700 West Front Street
Statesville, North Carolina                                         28677
---------------------------                                         -----
(Address of principal executive offices)                         (Zip Code)

                                (704) 873-7202
                                --------------
             (Registrant's telephone number, including area code)

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 December 04, 1998, the Registrant had outstanding 2,436,296 shares of
Common Stock.

Pages: This report, including exhibits, contains 14 pages numbered sequentially
from this cover page.
<PAGE>
 

                        KEWAUNEE SCIENTIFIC CORPORATION

                              INDEX TO FORM 10-Q

                FOR THE QUARTERLY PERIOD ENDED October 31, 1998

<TABLE>
<CAPTION>
                                                                           Page
                                                                          Number
                                                                          ------
<S>                                                                       <C>
PART I.  FINANCIAL INFORMATION
------------------------------

Item 1. Financial Statements
 
        Condensed Statements of Operations -
         Three and six months ended October 31, 1998 and 1997                  3
 
        Condensed Balance Sheets - October 31, 1998
         and April 30, 1998                                                    4
                                                                
        Condensed Statements of Cash Flows -                    
         Six months ended October 31, 1998 and 1997                            5
                                                                
        Notes to Condensed Financial Statements                                6
 
Item 2. Management's Discussion and Analysis of Financial
        Condition and Results of Operations                                    7
 
Review by Independent Accountants                                             11
 
Independent Accountants' Report                                               12
 
PART II. OTHER INFORMATION
--------------------------

Item 4. Submission of Matters to a Vote of Security Holders                   13
                                                           
Item 6. Exhibits and Reports on Form 8-K                                      13
                                                           
SIGNATURE                                                                     14
---------                                                      
</TABLE> 

                                       2
<PAGE>
 

                         Part 1. Financial Information

Item 1. Financial Statements

                        Kewaunee Scientific Corporation
                      Condensed Statements of Operations
                                  (Unaudited)

<TABLE>
<CAPTION>
                                       Three months ended     Six months ended
                                           October 31            October 31
                                           ----------            ----------
                                        1998        1997       1998      1997
                                        ----        ----       ----      ----
                                       ($ in thousands; except per share data)
<S>                                    <C>         <C>        <C>       <C>
                                    
Net sales                              $19,253     $18,442    $38,877   $36,104
                                    
Cost of products sold                   15,229      14,489     30,431    28,013
                                       -------     -------    -------   -------
                                    
Gross profit                             4,024       3,953      8,446     8,091
                                    
Operating expenses                       2,985       3,014      6,108     6,180
                                       -------     -------    -------   -------
                                    
Operating earnings                       1,039         939      2,338     1,911
                                    
Interest expense                           (14)        (47)       (26)      (99)
                                    
Other income (expense), net                (18)         11        (28)       22
                                       -------     -------    -------   -------
                                    
Earnings before income taxes             1,007         903      2,284     1,834
                                    
Income tax expense (benefit)               402         362        913       734
                                       -------     -------    -------   -------
                                    
Net earnings                           $   605     $   541    $ 1,371   $ 1,100
                                       =======     =======    =======   =======
                                    
Net earnings per share-             
    Basic                                $0.25       $0.23      $0.56     $0.46
    Diluted                              $0.25       $0.22      $0.56     $0.45
                                    
Average number of common            
shares outstanding (in thousands)-  
    Basic                                2,434       2,376      2,429     2,371
    Diluted                              2,466       2,436      2,462     2,421
</TABLE>

           See accompanying notes to condensed financial statements.

                                       3
<PAGE>
 
                        Kewaunee Scientific Corporation
                           Condensed Balance Sheets
                               ($ in thousands)

<TABLE>
<CAPTION>
                                                    October 31         April 30
                                                       1998              1998
                                                       ----              ----
                                                    (Unaudited)
<S>                                                 <C>                <C>
Assets                                                         
------                                                         
Currents assets:                                               
  Cash and cash equivalents                           $    120         $  1,809
  Receivables                                           15,395           13,819
  Inventories                                            3,584            3,710
  Deferred income taxes                                  1,240            1,240
  Prepaid expenses and other current assets                470              275
                                                      --------         --------
Total current assets                                    20,809           20,853
                                                      --------         --------
                                                               
Property, plant and equipment, at cost                  28,992           27,063
Accumulated depreciation                               (17,944)         (17,029)
                                                      --------         --------
Net property, plant and equipment                       11,048           10,034
                                                      --------         --------
Other assets                                             1,067              979
                                                      --------         --------
                                                               
Total Assets                                          $ 32,924         $ 31,866
                                                      ========         ========
                                                               
Liabilities and Stockholders' Equity                           
------------------------------------                           
Current liabilities:                                           
  Accounts payable                                       7,201            6,209
  Employee compensation and amounts withheld             1,469            2,439
  Other current liabilities                              2,472            2,639
                                                      --------         --------
Total current liabilities                               11,142           11,287
                                                      --------         --------
                                                               
Deferred income taxes                                      809              809
Accured employee benefit plan costs                        736              731
                                                      --------         --------
Total Liabilities                                       12,687           12,827
                                                      --------         --------
                                                               
Stockholders' equity:                                          
  Common stock                                           6,550            6,550
  Additional paid-in-capital                                86              144
  Retained earnings                                     14,696           13,568
  Common stock in treasury, at cost                     (1,095)          (1,223)
                                                      --------         --------
Total stockholders' equity                              20,237           19,039
                                                      --------         --------
                                                               
Total Liabilities and Stockholders' Equity            $ 32,924         $ 31,866
                                                      ========         ========
</TABLE>

           See accompanying notes to condensed financial statements.

                                       4
<PAGE>
 
                        Kewaunee Scientific Corporation
                      Condensed Statements of Cash Flows
                                  (Unaudited)
                               ($ in thousands)

<TABLE>
<CAPTION>
                                                           Six months ended
                                                              October 31
                                                              ----------
                                                          1998            1997
                                                          ----            ----
<S>                                                     <C>             <C>
Cash flows from operating activities:
Net earnings                                            $ 1,371         $ 1,100
Adjustments to reconcile net earnings to net
cash provided by (used in) operating activities:
  Depreciation and amortization                             926             779
  Provision for bad debts                                    96              41
  Increase in receivables                                (1,672)         (3,887)
  (Increase) decrease in inventories                        126          (1,354)
  Increase (decrease) in accounts payable
    and other current liabilities                          (145)          2,157
  Other, net                                               (280)             67
                                                        -------         -------
Net cash provided by (used in) operating activities         422          (1,097)
                                                        -------         -------

Cash flows from investing activities:
  Capital expenditures                                   (1,938)           (429)
                                                        -------         -------
Net cash used in investing activities                    (1,938)           (429)
                                                        -------         -------

Cash flows from financing activities:
  Net increase in short-term borrowings                      --           1,663
  Dividends paid                                           (243)           (190)
  Proceeds from exercise of stock options                   (70)             55
                                                        -------         -------
Net cash (used in) provided by financing activities        (173)          1,528
                                                        -------         -------

Increase (decrease) in cash and cash equivalents         (1,689)              2
                                                        -------         -------

Cash and cash equivalents, beginning of period            1,809               6
                                                        -------         -------

Cash and cash equivalents, end of period                $   120         $     8
                                                        =======         =======

Supplemental disclosure:
  Interest paid                                         $    25         $    88
  Income taxes paid                                     $ 1,356         $   833
</TABLE>

           See accompanying notes to condensed financial statements.

                                       5
<PAGE>
 
                        Kewaunee Scientific Corporation
                    Notes to Condensed Financial Statements
                                  (unaudited)


A.  Financial Information
-------------------------

The unaudited interim condensed financial statements of Kewaunee Scientific
Corporation (the "Company" or "Kewaunee") have been prepared pursuant to the
rules and regulations of the Securities and Exchange Commission (the
"Commission").  Accordingly, certain information and footnote disclosures
normally included in financial statements prepared in accordance with generally
accepted accounting principles have been condensed or omitted.  These interim
condensed financial statements should be read in conjunction with the financial
statements and notes included in the Company's 1998 Annual Report to
Stockholders.

The preparation of the financial statements in conformity with generally
accepted accounting principles requires management to make certain estimates and
assumptions that affect reported amounts and disclosures.  Actual results could
differ from those estimates.

In the opinion of management, the interim condensed financial statements reflect
all adjustments (consisting only of normal recurring adjustments) necessary for
a fair presentation of the interim periods.  The results of operations for the
interim periods are not necessarily indicative of the results of operations to
be expected for the full year.

B.  Inventories
---------------

Inventories consisted of the following (in thousands):
<TABLE>
<CAPTION>
 
                           October 31, 1998             April 30, 1998
                           ----------------             --------------
<S>                        <C>                          <C>
Finished products               $  598                      $1,020
Work-in-process                  1,035                       1,016
Raw materials                    1,951                       1,674
                                ------                      ------
 
                                $3,584                      $3,710
                                ======                      ======
</TABLE>

C.  Balance Sheet
-----------------

The Company's April 30, 1998 condensed balance sheet as presented herein is
derived from audited financial statements, but does not include all disclosures
required by generally accepted accounting principles.


                                       6
<PAGE>
 
          Item 2.  Management's Discussion and Analysis of Financial
                      Condition and Results of Operations


The Company's 1998 Annual Report to Stockholders contains management's
discussion and analysis of financial condition and results of operations at and
for the year ended April 30, 1998.  The following discussion and analysis
describes material changes in the Company's financial condition since April 30,
1998.  The analysis of results of operations compares the three months and six
months ended October 31, 1998 with the comparable periods of the prior fiscal
year.

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

The Company recorded sales of $19.3 million for the three months ended October
31, 1998, up 4.4% from sales of $18.4 million for the comparable period of the
prior year.  Sales for the six months ended October 31, 1998 were $38.9 million,
up 7.7% from sales of $36.1 million in the comparable period of the prior year.

The increases in sales for the quarter and six months ended October 31, 1998
resulted primarily from increased unit sales of steel and wood laboratory
furniture, partially offset by lower sales of technical products.

The gross profit margin for the quarter ended October 31, 1998 was 20.9% of
sales, as compared to 21.4% of sales in the comparable quarter of the prior
year.  The gross profit margin for the six months ended October 31, 1998 was
21.7% as compared to 22.4% in the comparable period of the prior year.  The
decreases in the gross profit margins in the current year resulted primarily
from start-up and other costs associated with the Company's new product lines.

Operating expenses for the quarter ended October 31, 1998 were $3.0 million, or
15.5% of sales, as compared to $3.0 million, or 16.3% of sales, in the
comparable quarter of the prior year. Operating expenses for the six months
ended October 31, 1998 were $6.1 million, or 15.7% of sales, as compared to $6.2
million, or 17.1% of sales, in the comparable period of the prior year. The
decreases in operating expenses as a percent of sales in the current year were
primarily attributable to a lower mix of commissionable sales, and to a lesser
extent, relatively flat levels of general and administrative expenses.

Operating earnings of $1.0 million and $2.3 million were recorded for the three
months and six months ended October 31, 1998, respectively.  This compares to
operating earnings of $939,000 and $1.9 million for the comparable periods of
the prior year.

Interest expense was $14,000 and $26,000 for the three months and six months
ended October 31, 1998, respectively, compared to $47,000 and $99,000 for the
comparable periods of the prior year.  The decreases in interest expense in the
current year resulted primarily from lower levels of debt under the Company's
revolving credit facility.


                                       7
<PAGE>
 

Other expenses were $18,000 and $28,000 for the three months and six months
ended October 31, 1998, respectively, compared to other income of $11,000 and
$22,000 for the comparable periods of the prior year.

Income tax expense of $402,000 and $913,000 was recorded for the three months
and six months ended October 31, 1998, respectively, as compared to income tax
expense of $362,000 and $734,000 recorded for the comparable periods of the
prior year. The effective tax rate was approximately 40% for each of the periods
in the current year and the prior year.

Net earnings of $605,000 and $1.4 million, or $.25 per diluted share and $.56
per diluted share, were recorded for the three months and six months ended
October 31, 1998, respectively. This compares to net earnings of $541,000 and
$1.1 million, or $.22 per diluted share and $.45 per diluted share,
respectively, for the comparable periods of the prior year.

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

Historically, the Company's principal sources of liquidity have been funds
generated from operations, supplemented as needed by short-term borrowings. The
Company believes that these sources will be sufficient to support ongoing
business levels, including capital expenditures.

The Company had working capital of $9.7 million at October 31, 1998, as compared
to $9.6 million at April 30, 1998. The ratio of current assets to current
liabilities was 1.9-to-1 at October 31, 1998 as compared to 1.8-to-1 at April
30, 1998. Although the Company has borrowings outstanding from time-to-time
based on its working capital needs, the Company did not have any outstanding
borrowings under its revolving credit facility at October 31, 1998 or at April
30, 1998.

The Company's operations provided cash of $422,000 during the six months ended
October 31, 1998, primarily from operating earnings, partially offset by an
increase in customer receivables. The Company's operations used cash of $1.1
million during the six months ended October 31, 1997, primarily to support
increases in customer receivables and inventory, partially offset by cash
provided by operating earnings and a net increase in accounts payable and other
current liabilities.

The Company used cash of $1.9 million for capital expenditures during the six
months ended October 31, 1998 and used cash of $429,000 for such expenditures
during the comparable period of the prior year, in both instances primarily for
the purchase of production machinery. The Company entered into operating lease
arrangements for production equipment with an aggregate original asset cost of
$549,000 during the six months ended October 31, 1997. These leases provide the
Company with certain early cancellation rights, as well as renewal, and purchase
options.

                                       8
<PAGE>
 

Year 2000
---------

The Year 2000 issue is the result of computer programs being written using two
digits rather than four to define the applicable year. Computer programs that
have date-sensitive software may recognize a date using "00" as the year 1900
rather than the year 2000. In the event that the Company's internal systems or
one or more significant suppliers or customers fail to achieve Year 2000
compliance, the Company's business and profitability could be adversely
affected.

The Company has completed an inventory and preliminary assessment of its
computer systems and application software and has determined that its main
business applications are Year 2000 compliant. Teams have been established to
implement plans to address Year 2000 issues for all other aspects of the
Company's business, including upgrading or replacing non-compliant software and
investigating the Year 2000 compliance of suppliers, customers and other
external entities. The Company does not yet have a formal contingency plan with
respect to suppliers, customers and other external entities, but will develop a
plan if determined necessary. A target date of April 30, 1999 has been set for
establishing compliance and developing any necessary contingency plans.
Accordingly, the Company has not yet determined the extent of the consequences,
if any, to the Company should a major supplier or customer fail to become Year
2000 compliant and if contingency procedures should need to be employed.

The Company has not incurred, nor does it expect to incur, significant costs in
addressing Year 2000 issues, as the Company's main business applications are
Year 2000 compliant. Any such costs, including internal staff costs and costs to
write-off unamortized hardware and software that may need to be replaced, will
generally be expensed as incurred. Although the Company is presently not aware
of any material exposures or contingencies related to the Year 2000 compliance
efforts of its significant vendors and business partners, if a significant
vendor or business partner should be non-compliant there can be no assurance
such an event will not have a material adverse effect on the Company's
consolidated financial position, results of operations and cash flows.

Recent Accounting Standards
---------------------------

The Financial Accounting Standards Board has issued Statement of Financial
Accounting Standards (SFAS) No. 131, "Disclosures about Segments of an
Enterprise and Related Information." This statement will be adopted as required
during the Company's 1999 fiscal year. SFAS No. 131 redefines how operating
segments are determined and requires disclosure of certain financial and
descriptive information about a company's operating segments. The Company has
not completed its evaluation of the effects that SFAS No. 131 will have on its
financial reporting and disclosures.

Safe Harbor Statement under the Private Securities Litigation Reform Act of 1995
--------------------------------------------------------------------------------

Certain statements in this report constitute "forward-looking" statements within
the meaning of the Private Securities Litigation Reform Act of 1995 (the "Reform
Act"). Such forward-looking statements involve known and unknown risks,
uncertainties and other factors that could

                                       9
<PAGE>
 

significantly impact results or achievements expressed or implied by such
forward-looking statements. These factors include, but are not limited to,
economic, competitive, governmental, and technological factors affecting the
Company's operations, markets, products, services, and prices. The cautionary
statements made pursuant to the Reform Act herein and elsewhere by the Company
should not be construed as exhaustive or as any admission regarding the adequacy
of disclosures made by the Company prior to the effective date of the Reform
Act. The Company cannot always predict what factors would cause actual results
to differ materially from those indicated by the forward-looking statements. In
addition, readers are urged to consider statements that include the terms
"believes", "belief", "expects", "plans", "objectives", "anticipates", "intends"
or the like to be uncertain and forward-looking.

                                      10
<PAGE>
 

REVIEW BY INDEPENDENT ACCOUNTANTS

A review of the interim financial information included in this Quarterly Report
on Form 10-Q for the three months and six months ended October 31, 1998 has been
performed by PricewaterhouseCoopers LLP, the Company's independent accountants.
Their report on the interim financial information follows. There have been no
adjustments or disclosures proposed by PricewaterhouseCoopers LLP which have not
been reflected in the interim financial information.

                                      11
<PAGE>
 

INDEPENDENT ACCOUNTANTS' REPORT

To the Board of Directors and Stockholders of
Kewaunee Scientific Corporation
Statesville, North Carolina

We have reviewed the accompanying condensed balance sheet of Kewaunee Scientific
Corporation as of October 31, 1998, and the related condensed statements of
operations for the three month and six month periods ended October 31, 1998, and
the condensed statement of cash flows for the six-month period ended October 31,
1998. These financial statements are the responsibility of the Company's
management.

We conducted our review in accordance with standards established by the American
Institute of Certified Public Accountants. A review of interim financial
information consists principally of applying analytical procedures to financial
data and of making inquiries of persons responsible for financial and accounting
matters. It is substantially less in scope than an audit conducted in accordance
with generally accepted auditing standards, the objective of which is the
expression of an opinion regarding the financial statements taken as a whole.
Accordingly, we do not express such an opinion.

Based on our review, we are not aware of any material modifications that should
be made to the accompanying condensed financial information for it to be in
conformity with generally accepted accounting principles.

We previously audited in accordance with generally accepted auditing standards,
the balance sheets as of April 30, 1998 and the related statements of income, of
retained earnings, and of cash flows for the year then ended (not presented
herein), and in our report dated June 1, 1998 we expressed an unqualified
opinion on those financial statements. In our opinion, the information set forth
in the accompanying condensed balance sheet as of April 30, 1998, is fairly
stated in all material respects in relation to the balance sheet from which it
was derived.


PricewaterhouseCoopers LLP
Charlotte, North Carolina
November 12, 1998

                                      12
<PAGE>
 

                          PART II. OTHER INFORMATION


Item 4. Submission of Matters to a Vote of Security Holders

     The Company's Annual Meeting of Stockholders was held on August 26, 1998.
     Information regarding the results of this meeting are incorporated by
     reference from the Company's Report on Form 10-Q for the three months ended
     July 31, 1998.

Item 6. Exhibits and Reports on Form 8-K

     (a)  Exhibits

          Exhibit 27  Financial Data Schedule

     (b)  Reports on Form 8-K

          No reports on Form 8-K were filed with the Commission during the three
          months ended October 31, 1998.

                                      13
<PAGE>
 

                                   SIGNATURE


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


                                                 KEWAUNEE SCIENTIFIC CORPORATION
                                                 -------------------------------

                                                          (Registrant)


Date: December 11, 1998                          By /s/ D. Michael Parker
                                                    -------------------------
                                                    D. Michael Parker
                                                    Vice President of Finance
                                                    Chief Financial Officer

                                      14