<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, 1999

 
[_]   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 26, 1999, the Registrant had outstanding 2,436,296 shares of
Common Stock.

Pages: This report, including exhibits, contains 16 pages numbered sequentially
from this cover page.
<PAGE>
 
                        KEWAUNEE SCIENTIFIC CORPORATION

                               INDEX TO FORM 10-Q

                FOR THE QUARTERLY PERIOD ENDED January 31, 1999

<TABLE>
<CAPTION>
                                                                        Page
                                                                       Number
                                                                       ------
<S>                                                                    <C>

PART I.  FINANCIAL INFORMATION
------------------------------
 
Item 1.  Financial Statements
 
              Condensed Statements of Operations -
               Three and nine months ended January 31, 1999 and 1998      3
 
              Condensed Balance Sheets - January 31, 1999
               and April 30, 1998                                         4
 
              Condensed Statements of Cash Flows -
                Nine months ended January 31, 1999 and 1998               5
 
              Notes to Condensed Financial Statements                     6
 
 
Item 2.  Management's Discussion and Analysis of Financial
          Condition and Results of Operations                             8
 
Review of Independent Accountants                                        13
 
Report of Independent Accountants                                        14
 
PART II.  OTHER INFORMATION
---------------------------

Item 6. Exhibits and Reports on Form 8-K                                 15


SIGNATURE                                                                16
---------                                                           
</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
                                                        ----------------------    --------------------
                                                            1999        1998        1999         1998
                                                        ----------    --------    --------    --------
                                                           ($ in thousands, except per share data)
        <S>                                             <C>           <C>         <C>         <C>
         Net sales                                        $ 18,404    $ 17,333    $ 57,281    $ 53,437
         Cost of products sold                              14,302      12,990      44,733      41,003
                                                        ----------    --------    --------    --------
         Gross profit                                        4,102       4,343      12,548      12,434
         Operating expenses                                  3,000       3,345       9,108       9,525
                                                        ----------    --------    --------    --------
         Operating earnings                                  1,102         998       3,440       2,909
         Interest expense                                      (37)        (37)        (63)       (136)
         Other income (expense), net                            (5)         10         (33)         32
                                                        ----------    --------    --------    --------
         Earnings before income taxes                        1,060         971       3,344       2,805
         Income tax expense                                    425         388       1,338       1,122
                                                        ----------    --------    --------    --------
         Net earnings                                     $    635    $    583    $  2,006    $  1,683
                                                        ==========    ========    ========    ========
         Net earnings per share-
            Basic                                            $0.26       $0.24       $0.83    $   0.71
            Diluted                                          $0.26       $0.23       $0.81    $   0.68

           Average number of common shares
            outstanding (in thousands)-
            Basic                                            2,436       2,395       2,431       2,378
            Diluted                                          2,467       2,483       2,464       2,457
</TABLE>


         See accompanying notes to condensed financial statements.

                                       3
 
<PAGE>

                        Kewaunee Scientific Corporation
                           Condensed Balance Sheets
                               ($ in thousands)
<TABLE> 
<CAPTION> 
                                                   January 31   April 30
                                                      1999        1998
                                                   -----------  ---------
<S>                                                <C>          <C> 
Assets                                             (Unaudited)
------
Current assets:
  Cash and cash equivalents                        $      500   $   1,809
  Receivables                                          16,456      13,819
  Inventories                                           3,580       3,710
  Deferred income taxes                                 1,240       1,240
  Prepaid expenses and other current assets               466         275
                                                   ----------   ---------       
Total current assets                                   22,242      20,853
                                                   ----------   ---------

Property, plant and equipment, at cost                 29,988      27,063
Accumulated depreciation                              (18,245)    (17,029)
                                                   ----------   ---------
Net property, plant and equipment                      11,743      10,034
                                                   ----------   ---------
Other assets                                            1,041         979
                                                   ----------   ---------

Total Assets                                       $   35,026   $  31,866
                                                   ==========   =========

Liabilities and Stockholders' Equity
------------------------------------   
Current liabilities:
  Short-term borrowings                                 2,422           0
  Accounts payable                                      5,850       6,209
  Employee compensation and amounts withheld            1,733       2,439
  Other current liabilities                             2,745       2,639
                                                   ----------   ---------
Total current liabilities                              12,750      11,287
                                                   ----------   ---------

Deferred income taxes                                     809         809
Accrued employee benefit plan costs                       741         731
                                                   ----------   ---------
Total Liabilities                                      14,300      12,827
                                                   ----------   ---------


Stockholders' equity:
  Common stock                                          6,550       6,550
  Additional paid-in-capital                               86         144
  Retained earnings                                    15,185      13,568
  Common stock in treasury, at cost                    (1,095)     (1,223)
                                                   ----------   ---------
Total stockholders' equity                             20,726      19,039
                                                   ----------   ---------

Total Liabilities and Stockholders' Equity         $   35,026   $  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> 


                                                           Nine months ended
                                                              January 31
                                                           -----------------  
                                                            1999      1998
                                                           -------   -------  
<S>                                                        <C>       <C> 
Cash flows from operating activities:
Net earnings                                               $ 2,006   $ 1,683
Adjustments to reconcile net earnings to net cash
provided by (used in) operating activities:                 
  Depreciation and amortization                              1,262     1,115
  Provision for bad debts                                      107        81
  Increase in receivables                                  (2,744)   (2,344)
  (Increase) decrease in inventories                           130   (2,337)
  Increase (decrease) in accounts payable and
    other current liabilities                                (959)     2,009
  Other, net                                                 (245)       233
                                                           --------   --------
Net cash provided by (used in) operating activities          (443)       440
                                                           --------   -------- 

Cash flows from investing activities:
  Capital expenditures                                     (2,969)     (816)
                                                           --------   -------- 
Net cash used in investing activities                      (2,969)     (816)
                                                           --------   -------- 
Cash flows from financing activities:
  Net increase in short-term borrowings                      2,422       572
  Dividends paid                                             (389)     (309)
  Proceeds from exercise of stock options                       70       114
                                                           --------   --------
Net cash provided by financing activities                    2,103       377
                                                            -------   --------

Increase (decrease) in cash and cash equivalents           (1,309)         1

Cash and cash equivalents, beginning of period               1,809         6
                                                           --------   --------
Cash and cash equivalents, end of period                   $   500   $     7
                                                           ========   ========
Supplemental disclosure:
  Interest paid                                                $49      $128
  Income taxes paid                                         $1,732    $1,145

</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>
                          January 31, 1999  April 30, 1998
                          ----------------  --------------
<S>                       <C>               <C>
Finished products              $  629          $1,020
Work-in-process                 1,145           1,016
Raw materials                   1,806           1,674
                               ------          ------
 
                               $3,580          $3,710
                               ======          ======
</TABLE>

                                       6
<PAGE>
 
C.  Financing Arrangements
--------------------------

On January 6, 1999, the Company entered into a new credit facility, replacing
the Company's previous $8.5 million two-year secured revolving credit facility
with another lender which expired on that date.  The new facility allows the
Company to borrow up to $3 million under a two-year unsecured revolving credit
component and up to $5 million under a seven-year equipment loan component.  All
advances under the equipment loan component must be made during the first two
years of the agreement and must be secured by qualifying machinery and
equipment.

The Company provides monthly interest payments under both components of the
facility calculated at the lower of (1) the LIBOR Market Index Rate plus 1.75%,
or (2) the lender's Prime Rate minus .75%.  Beginning in the third year of the
equipment loan, monthly principal payments will be required in sixty equal
installments.  The equipment loan includes financial covenants with respect to
the Company's tangible net worth, funds flow coverage, current ratio, and ratio
of liabilities to tangible net worth.

At January 31, 1999, advances of $2.4 million were outstanding under the
revolving credit loan.  No advances were outstanding under the equipment loan.

                                       7
<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 nine
months ended January 31, 1999 with the comparable periods of the prior fiscal
year.

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

The Company recorded sales of $18.4 million for the three months ended January
31, 1999, up 6.2% from sales of $17.3 million for the comparable period of the
prior year.  Sales for the nine months ended January 31, 1999 were $57.3
million, up 7.2% from sales of $53.4 million in the comparable period of the
prior year.

The sales improvements over the prior year periods resulted primarily from
increased unit sales of laboratory furniture, as continued strong demand for
these products more than offset the impact of a weaker technical furniture
marketplace during the  current year periods.

The gross profit margin for the quarter ended January 31, 1999 was 22.3% of
sales, as compared to 25.1% of sales in the comparable quarter of the prior
year. The gross profit margin for the nine months ended January 31, 1999 was
21.9%, as compared to 23.3% in the comparable period of the prior year.  The
decreases in the gross profit margins in the current year resulted primarily
from continuing start-up and other costs associated with the Company's new
product lines, particularly in the second quarter of the current year, and to a
lesser extent, in the third quarter of the current year.

Operating expenses for the quarter ended January 31, 1999 were $3.0 million, or
16.3% of sales, as compared to $3.3 million, or 19.3% of sales, in the
comparable quarter of the prior year. Operating expenses for the nine months
ended January 31, 1999 were $9.1 million, or 15.9% of sales, as compared to $9.5
million, or 17.8% of sales, in the comparable period of the prior year.  The
decreases in operating expenses in the current year were primarily attributable
to reduced sales commissions, resulting from lower commissionable sales, and
lower administrative expenses.

                                       8
<PAGE>
 
Operating earnings of $1.1 million and $3.4 million were recorded for the three
months and nine months ended January 31, 1999, respectively.  This compares to
operating earnings of $1.0 million and $2.9 million for the comparable periods
of the prior year.

Interest expense was $37,000 and $63,000 for the three months and nine months
ended January 31, 1999, respectively, compared to $37,000 and $136,000 for the
comparable periods of the prior year.  The decreases in interest expense for the
current year resulted primarily from lower levels of borrowings under the
Company's revolving credit facility.

Other expenses were $5,000 and $33,000 for the three months and nine months
ended January 31, 1999, respectively, compared to other income of $10,000 and
$32,000 for the comparable periods of the prior year.

Income tax expense of $425,000 and $1.3 million was recorded for the three
months and nine months ended January 31, 1999, respectively, compared to income
tax expense of $388,000 and $1.1 million 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 $635,000 and $2.0 million, or $.26 cents per diluted share and
$.81 cents per diluted share, were recorded for the three months and nine months
ended January 31, 1999, respectively.  This compares to net earnings of $583,000
and $1.7 million, or $.23 cents per diluted share and $.68 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's new credit facility, which is more fully described in the notes to the
condensed financial statements, is available to support short-term needs, as
well as longer-term financing for machinery and other capital needs.  The
Company believes that these sources will be sufficient to support ongoing
working capital needs.

                                       9
<PAGE>
 
The Company had working capital of $9.5 million at January 31, 1999, as compared
to $9.6 million at April 30, 1998.  The ratio of current assets to current
liabilities was 1.74-to-1 at January 31, 1999, as compared to 1.85-to-1 at April
30, 1998.  The debt-to-equity ratio was .12-to-1 at January 31, 1999; the
Company had no debt at April 30, 1998.  At January 31, 1999, the Company had
outstanding borrowings of $2.4 million under the revolving credit component of
its new credit facility.

The Company's operations used cash of $443,000 during the nine months ended
January 31, 1999, primarily to support increases in customer receivables and
reductions in accounts payable and other current liabilities.  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 used cash of $3.0 million for capital expenditures during the nine
months ended January 31, 1999 and used cash of $816,000 for such expenditures
during the comparable period of the prior year, in both instances primarily for
the purchase of production machinery.  The increase in capital expenditures for
the current year is part of a strategy to invest heavily in computerized
machinery at the Company's Statesville operations to improve manufacturing
efficiencies and reduce costs.

An increase in short-term borrowings during the nine months ended January 31,
1999 provided cash of $2.4 million, as compared to an increase of $572,000 in
these borrowings in the comparable period of the prior year.  Cash dividends in
the amount of $389,000 were paid during the nine months ended January 31, 1999,
as compared to dividends paid of $309,000 for the comparable period of the prior
year.

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.

                                       10
<PAGE>
 
The Company has completed an inventory and assessment of its computer systems
and application software and has determined that its main business applications
are Year 2000 compliant.  An action plan is well underway to address Year 2000
issues for smaller applications and all other aspects of the Company's business.
Actions include upgrading or replacing non-compliant software and monitoring the
Year 2000 compliance of suppliers, customers and other external entities.  The
Company is on schedule to meet its internal target date of April 30, 1999 for
establishing compliance.

The Company has not yet determined the extent of the consequences, if any, to
the Company should one or more of its significant suppliers or business partners
fail to become Year 2000 compliant, and, accordingly, has not determined if any
contingency plan with respect to these entities is needed.  The Company is
presently not aware of any material exposures or contingencies related to the
Year 2000 compliance efforts of its significant suppliers and business partners.
However, if a significant supplier or business partner should be non-compliant,
there can be no assurance that such an event will not have a material adverse
effect on the Company's consolidated financial position, results of operations
and cash flows.

The Company has not incurred, nor does it expect to incur, significant costs in
addressing Year 2000 issues.

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 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.

                                       11
<PAGE>
 
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
at the end of 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.

                                       12
<PAGE>
 
                       REVIEW OF 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, 1999 has
been performed by PricewaterhouseCoopers LLP, the Company's independent
accountants.  Their report on the interim financial information follows.  There
have been no adjustments proposed by PricewaterhouseCoopers LLP which have not
been reflected in the interim financial information.

                                       13

<PAGE>
 
                       REPORT OF INDEPENDENT ACCOUNTANTS

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, 1999, and the related condensed statements of
operations for the three-month and nine-month periods ended January 31, 1999,
and the condensed statement of cash flows for the nine-month period ended
January 31, 1999.  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
February 12, 1999

                                       14
<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, 1999.

                                       15

<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, 1999                      By   /s/ D. Michael Parker
                                             --------------------------------
                                              D. Michael Parker
                                              Vice President of Finance
                                              Chief Financial Officer

                                       16