<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 January 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 February 27, 1998, the Registrant had outstanding 2,407,046 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 January 31, 1998

<TABLE> 
<CAPTION> 
                                                                       Page
                                                                      Number
                                                                      ------
PART I.  FINANCIAL INFORMATION
------------------------------
<S>                                                                   <C>   
Item 1.   Financial Statements
 
          Condensed Statements of Operations -
           Three and nine months ended January 31, 1998 and 1997           3
 
          Condensed Balance Sheets - January 31, 1998
           and April 30, 1997                                              4
 
          Condensed Statements of Cash Flows -
           Nine months ended January 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 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   Nine months ended     
                                     January 31          January 31   
                               --------------------  -----------------   
                                   1998      1997      1998     1997    
                               ----------- --------  -------- --------   
                               ($ in thousands, except per share data)    
<S>                            <C>         <C>       <C>      <C> 
Net sales                         $17,333  $14,837   $53,437  $47,045    
Cost of products sold              12,990   11,353    41,003   36,532    
                               ----------- --------  -------- --------   
Gross profit                        4,343    3,484    12,434   10,513    
Operating expenses                  3,345    2,918     9,525    8,756    
                               ----------- --------  -------- --------   
Operating earnings                    998      566     2,909    1,757    
Interest expense                      (37)     (68)     (136)    (311)   
Other income, net                      10       12        32       31    
                               ----------- --------  -------- --------   
Earnings before income taxes          971      510     2,805    1,477    
Income tax  expense (benefit)         388      (35)    1,122     (365)   
                               ----------- --------  -------- --------   
                                                                          
Net earnings                      $   583  $   545   $ 1,683  $ 1,842    
                               =========== ========  ======== ========   
                                                                          
Net earnings per share                                                    
     Basic                        $  0.24  $  0.23   $  0.71  $  0.78    
     Diluted                      $  0.23  $  0.22   $  0.68  $  0.77    
                                                                          
Average number of common shares                                           
  outstanding (in thousands)                                              
     Basic                          2,395    2,366     2,378    2,366
     Diluted                        2,483    2,424     2,457    2,401
</TABLE> 

    See accompanying notes to condensed financial statements.

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

<TABLE> 
<CAPTION> 
                                         January 31     April 30
                                            1998          1997 
                                         ----------     --------
ASSETS                                  (Unaudited)             
------                                                          
<S>                                     <C>             <C>     
Current assets:                                                 
  Cash                                      $     7      $     6
  Receivables                                15,127       12,864
  Inventories                                 4,283        1,946
  Prepaid expenses and                                          
   other current assets                       1,420        1,649
                                         ----------     --------
Total current assets                         20,837       16,465
                                         ----------     -------- 

Property, plant and equipment, at cost       27,142       26,431
Accumulated depreciation                    (17,615)     (16,605)
                                         ----------     --------
Net property, plant and equipment             9,527        9,826
                                         ----------     --------
Other assets                                    687          700
                                         ----------     --------
                                                               
                                            $31,051      $26,991
                                         ==========     ======== 

LIABILITIES  AND  STOCKHOLDERS'  EQUITY
---------------------------------------
Current liabilities:
  Short-term borrowings                     $   572      $     -
  Accounts payable                            5,928        5,136
  Other current liabilities                   5,541        4,324
                                         ----------     --------
Total current liabilities                    12,041        9,460
                                         ----------     --------

Deferred income taxes and other
   non-current liabilities                      936          945
                                         ----------     --------
Stockholders' equity:
  Common stock                                6,550        6,550
  Additional paid-in-capital                     59          116
  Retained earnings                          12,809       11,435
  Common stock in treasury, at cost          (1,344)      (1,515)
                                         ----------     --------
Total stockholders' equity                   18,074       16,586
                                         ----------     --------

                                            $31,051      $26,991
                                         ==========     ========
</TABLE> 

See accompanying notes to condensed financial statements.


                                       4

<PAGE>

                        Kewaunee Scientific Corporation
                      Condensed Statements of Cash Flows
                               ($ in thousands)

<TABLE> 
<CAPTION> 
                                                          Nine months ended     
                                                                January 31  
                                                          ------------------    
                                                            1998      1997      
                                                          --------  --------    
                                                              (Unaudited) 
<S>                                                       <C>       <C> 
CASH FLOWS FROM OPERATING ACTIVITIES:                                          
Net earnings                                               $1,683    $1,842    
Adjustments to reconcile net earnings to net cash                              
provided by (used in) operating activities:                                    
  Depreciation and amortization                             1,115     1,269    
  Provision for bad debts                                      81       194    
  (Increase) decrease in receivables                       (2,344)      719    
  Increase in inventories                                  (2,337)   (1,485)   
  Increase in accounts payable and                                             
    other current liabilities                               2,009       417    
  Other, net                                                  233      (365)   
                                                          -------   -------
Net cash provided by operating activities                     440     2,591    
                                                          -------   -------
                                                                               
CASH FLOWS FROM INVESTING ACTIVITIES:                                          
  Capital expenditures                                       (816)   (1,292)   
                                                          -------   -------
Net cash used in investing activities                        (816)   (1,292)   
                                                          -------   -------
                                                                               
CASH FLOWS FROM FINANCING ACTIVITIES:                                          
  Net increase (decrease) in short-term borrowings            572    (1,173)   
  Dividends paid                                             (309)      (95)   
  Proceeds from exercised stock options                       114         -    
  Repayment of long-term debt                                   -       (41)   
                                                          -------   -------
Net cash provided by (used in) financing activities           377    (1,309)   
                                                          -------   -------
INCREASE (DECREASE) IN CASH                                     1       (10)   
CASH, BEGINNING OF PERIOD                                       6        16    
                                                          -------   -------
                                                                               
CASH, END OF PERIOD                                            $7        $6    
                                                          =======   =======

SUPPLEMENTAL DISCLOSURE:
  Interest paid                                              $128      $275
  Income taxes paid                                        $1,145       $12
</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 1997 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>
                                   January 31, 1998  April 30, 1997
                                   ----------------  --------------
<S>                                <C>               <C>           
Finished products                      $1,054              $  366 
Work-in-process                         1,190                 638 
Raw materials                           2,039                 942 
                                       ------              ------ 
                                                                  
                                       $4,283              $1,946 
                                       ======              ======  
</TABLE>

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

The Company's April 30, 1997 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 1997 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, 1997.  The following discussion and analysis
describes material changes in the Company's financial condition since April 30,
1997.  The analysis of results of operations compares the three months and nine
months ended January 31, 1998 with the comparable periods of the prior fiscal
year.

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

The Company recorded sales of $17.3 million for the three months ended January
31, 1998, up 16.8% from sales of $14.8 million for the comparable period of the
prior year.  Sales for the nine months ended January 31, 1998 were $53.4
million, up 13.6% from sales of $47.0 million in the comparable period of the
prior year.

The increases in sales for the quarter and nine months ended January 31, 1998
resulted primarily from sales of furniture in the Company's Research Collection
introduced late in the previous fiscal year, increased sales of epoxy resin
worksurfaces, and selling price increases.  Sales for the quarter also benefited
from the timing of shipments under several contract orders.

The gross profit margin for the quarter ended January 31, 1998 was 25.1% of
sales, as compared to 23.5% of sales in the comparable quarter of the prior
year.  The improvement in the gross profit margin for the quarter resulted
primarily from an improved product sales mix, improved profit margins on
contract-bid laboratory furniture sales, and manufacturing efficiencies realized
from increased production volumes.

The gross profit margin for the nine months ended January 31, 1998 was 23.3%, up
from 22.3% in the comparable period of the prior year.  The improvement in the
gross profit margin for the nine months ended January 31, 1998 resulted
primarily from an improved product sales mix and improved profit margins on
contract-bid laboratory furniture sales as discussed above.  However, the
favorable impact of these items was partially offset by increased costs in the
second quarter of the current year.  In

                                       7
<PAGE>
 
that quarter, the Company experienced increased labor costs resulting from the
expansion of production capacity and incurred higher costs when certain
component parts normally manufactured by the Company were purchased until
production capacity could be expanded to handle the increased demand.

Operating expenses for the quarter ended January 31, 1998 were $3.3 million, or
19.3% of sales, as compared to $2.9 million, or 19.7% of sales, in the
comparable quarter of the prior year. Operating expenses for the nine months
ended January 31, 1998 were $9.5 million, or 17.8% of sales, as compared to $8.8
million, or 18.6% of sales, in the comparable period of the prior year.  The
increases in operating expenses for the quarter and nine months of the current
year were primarily attributable to increased sales and marketing costs,
including sales commissions associated with the increases in sales.  The
increases in these costs for the nine months of the current year were partially
offset by decreases in depreciation expense and bad debt expense.  As a percent
of sales, operating expenses for the quarter and nine months of the current year
benefited from the current year increases in sales volumes and the reduced
depreciation and bad debt expenses.

Operating earnings of $998,000 and $2.9 million were recorded for the three
months and nine months ended January 31, 1998, respectively.  This compares to
operating earnings of $566,000 and $1.8 million for the comparable periods of
the prior year.

Interest expense was $37,000 and $136,000 for the three months and nine months
ended January 31, 1998, respectively, compared to $68,000 and $311,000 for the
comparable periods of the prior year.  The decreases in interest expense for the
current quarter and nine months of the current year resulted from lower levels
of borrowings under the Company's revolving credit facility.

Other income, consisting principally of royalty income, was $10,000 and $32,000
for the three months and nine months ended January 31, 1998, respectively,
compared to $12,000 and $31,000 for the comparable periods of the prior year.

Income tax expense of $388,000 and $1.1 million was recorded for the three
months and nine months ended January 31, 1998, respectively, as contrasted with
income tax benefits of $35,000 and $365,000 recorded for the comparable periods
of the prior year.  The income tax benefits reported for the comparable periods
of the prior year resulted from the reductions in the Company's valuation
allowance on deferred tax assets.  These

                                       8
<PAGE>
 
reductions occurred as continued profitability and an improved earnings outlook
for the Company provided further positive evidence to support a reduction in the
valuation allowance.

Net earnings of $583,000 and $1.7 million, or 23 cents per diluted share and 68
cents per diluted share, were recorded for the three months and nine months
ended January 31, 1998, respectively.  This compares to net earnings of $545,000
and $1.8 million, or 23 cents per diluted share and 77 cents 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 $8.8 million at January 31, 1998, as compared
to $7.0 million at April 30, 1997.  The ratio of current assets to current
liabilities was 1.7-to-1 at January 31, 1998, unchanged from April 30, 1997.
The debt-to-equity ratio was .03-to-1 at January 31, 1998; the Company had no
debt at April 30, 1997.  The Company had unused credit available under its
revolving credit facility of $7.7 million at January 31, 1998, as compared to
unused credit available under this facility of $8.0 million at April 30, 1997.

The Company's operations provided cash of $440,000 during the nine months ended
January 31, 1998, primarily from operating earnings and an increase in accounts
payable and other current liabilities, offset by increases in customer
receivables and inventories.  The Company's operations provided cash of $2.6
million during the nine months ended January 31, 1997, primarily from operating
earnings and a decrease in customer receivables, partially offset by an increase
in inventories.

An increase in short-term borrowings during the nine months ended January 31,
1998 provided cash of $572,000, while a reduction in these borrowings in the
comparable period of the prior year used cash of $1.2 million.  Cash dividends
in the amount of $309,000 were paid during the nine months ended January 31,
1998, as compared to dividends paid of $95,000 for the comparable period of the
prior year.

                                       9
<PAGE>
 
The Company used cash of $816,000 for capital expenditures during the nine
months ended January 31, 1998 and used cash of $1.3 million for such
expenditures during the comparable period of the prior year, in both instances
primarily for the purchase of production machinery.  In addition, the Company
entered into operating lease arrangements for production equipment with an
aggregate original asset cost of $549,000 and $80,000 during the nine months
ended January 31, 1998 and 1997, respectively.  These leases provide the Company
with certain early cancellation rights, as well as renewal, and purchase
options.  The Company does not anticipate an abnormal level of cash requirements
resulting from capital expenditures for the remainder of the current year.

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

Certain statements included in this report are forward looking and involve risk
and uncertainties that could significantly impact results.  These factors
include, but are not limited to, economic, competitive, governmental, and
technological factors affecting the Company's operations, markets, products,
services, and prices.

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

In February 1997, the FASB issued Statement of Financial Accounting Standard No.
128, "Earnings Per Share" ("Statement 128").  Statement 128 is effective for
financial statements issued for periods ending after December 15, 1997.
Statement 128 establishes standards for computing and presenting earnings per
share ("EPS"), simplifies the standards previously found in APB No. 15,
"Earnings Per Share," and makes them comparable to International EPS Standards.
In January 1998, the Company adopted the provisions of Statement 128.  Earnings
per share for all prior periods included in this report have been restated to
reflect the provisions of this Statement.

                                       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 nine months ended January 31, 1998 has
been performed by Price Waterhouse LLP, the Company's independent accountants.
Their report on the interim financial information follows.  There have been no
adjustments or disclosures proposed by Price Waterhouse 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 January 31, 1998, and the related condensed statements of
operations for the three-month and nine-month periods ended January 31, 1998,
and the condensed statement of cash flows for the nine-month period ended
January 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.

The accompanying condensed statements of operations and cash flows for the
three-month and nine-month periods ended January 31, 1997 were reviewed by other
independent accountants whose report dated February 13, 1997 stated that, based
upon their review, they were not aware of any material modifications that should
be made to the financial statements for them to be in conformity with generally
accepted accounting principles.  The financial statements for the year ended
April 30, 1997 were audited by the same independent accountants whose report
dated June 4, 1997 expressed an unqualified opinion on those statements.



Price Waterhouse LLP
Charlotte, North Carolina
February 13, 1998

                                       12
<PAGE>
 
                          PART II.  OTHER INFORMATION


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

                                       14