<PAGE>   1
================================================================================
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 10-Q
(Mark One)

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

    For the quarterly period ended December 31, 1998

                                       OR

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

    For the transition period from            to 
                                   -----------   ---------

                         Commission file number 0-28194

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

<TABLE>
<S>                                                <C>
                    DELAWARE                                            52-1536128                    
   -----------------------------------------       ---------------------------------------------------
        (State or other jurisdiction of                    (I.R.S. Employer Identification No.)
         incorporation or organization)

           9000 VIRGINIA MANOR ROAD
               BELTSVILLE, MARYLAND                                       20705     
--------------------------------------------------                   ---------------
   (Address of principal executive offices)                            (Zip Code)
</TABLE>

Registrant's telephone number, including area code (301) 470-6500
                                                   --------------

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

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

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

<TABLE>
<CAPTION>
                                                  Shares outstanding as of
                Class                                 February 10, 1999     
--------------------------------------            ---------------------------
<S>                                                        <C>
Common Stock, par value $.01 per share                     14,331,321
</TABLE>

================================================================================
<PAGE>   2
                               DIGENE CORPORATION

                               INDEX TO FORM 10-Q

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

      Item 1.    Consolidated Financial Statements -

             Consolidated Balance Sheets -
                   December 31, 1998 and June 30, 1998                                                1

             Consolidated Statements of Operations -
                   Three months ended December 31, 1998 and 1997;
                   Six months ended December 31, 1998 and 1997;                                       2

             Consolidated Statements of Cash Flows -
                   Six months ended December 31, 1998 and 1997                                        3

             Notes to Consolidated Financial Statements                                               4

      Item 2.    Management's Discussion and Analysis of Financial Condition and
                 Results of Operations                                                                5

PART II.  OTHER INFORMATION:

      Item 6.    Exhibits and Reports on Form 8-K                                                     9

SIGNATURES                                                                                           10

EXHIBIT INDEX                                                                                        11
</TABLE>





<PAGE>   3
PART I.  CONSOLIDATED FINANCIAL INFORMATION

ITEM 1.

                               DIGENE CORPORATION
                          CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                       DECEMBER 31,               JUNE 30,
                                                                           1998                     1998
                                                                      -----------------       ------------------
                                                                       (UNAUDITED)
                                ASSETS
 <S>                                                                  <C>                     <C>
 Current assets:
    Cash and cash equivalents                                         $      7,238,847        $      18,330,803
    Short-term investments                                                  11,917,774                7,181,572
    Accounts receivable, less allowance of approximately $209,000 at
       December 31, 1998 and June 30, 1998, respectively                     2,856,027                3,072,224
    Inventories                                                              3,906,546                3,557,289
    Prepaid expenses and other current assets                                1,887,519                  560,706
                                                                      -----------------       ------------------

 Total current assets                                                       27,806,713               32,702,594

 Property and equipment, net                                                 2,346,346                2,627,244
 Intangible assets, net                                                      1,438,601                   12,784
 Deposits                                                                      130,862                   96,916
                                                                      -----------------       ------------------

 Total assets                                                         $     31,722,522        $      35,439,538
                                                                      =================       ==================

                 LIABILITIES AND STOCKHOLDERS' EQUITY


 Current liabilities:
    Accounts payable                                                  $      2,549,134        $       2,424,245
    Accrued expenses                                                           684,015                  542,064
    Accrued payroll                                                            616,174                  755,490
    Current maturities of long-term debt                                             -                  552,717
                                                                      -----------------       ------------------

 Total current liabilities                                                   3,849,323                4,274,516

 Accrued rent                                                                   30,358                   54,340
 Deferred rent                                                                       -                   11,980

 Stockholders' equity:
    Common stock, $.01 par value, 50,000,000 shares authorized,
      14,331,321 and 14,117,308 shares issued and outstanding at 
      December 31, 1998 and June 30, 1998, respectively                        143,313                  141,173

    Additional paid-in capital                                              71,943,599               70,373,310
    Accumulated deficit                                                    (44,244,071)             (39,415,781)
                                                                      -----------------       ------------------

 Total stockholders' equity                                                 27,842,841               31,098,702
                                                                      -----------------       ------------------

 Total liabilities and stockholders' equity                           $     31,722,522        $      35,439,538
                                                                      =================       ==================
</TABLE>





                                       1
<PAGE>   4
                               DIGENE CORPORATION
                     CONSOLIDATED STATEMENTS OF OPERATIONS


<TABLE>
<CAPTION>
                                                        THREE MONTHS ENDED                             SIX MONTHS ENDED
                                                           DECEMBER 31,                                   DECEMBER 31,
                                            -----------------------------------------        ---------------------------------------
                                                     1998                   1997                    1998                   1997
                                            -----------------       -----------------        ----------------       ----------------
 <S>                                        <C>                     <C>                      <C>                    <C>
 Revenues:

    Product sales                           $      3,852,769        $      2,944,227         $     7,456,976        $     5,456,237
    Research and development contracts               153,861                  12,600                 153,861                 26,500
                                            -----------------       -----------------        ----------------       ----------------

 Total revenues                                    4,006,630               2,956,827               7,610,837              5,482,737

 Costs and expenses:
    Cost of product sales                          1,428,566                 834,838               2,404,555              1,549,249
    Research and development                       1,185,133               1,287,843               2,216,546              2,278,982
    Selling and marketing                          2,653,593               1,888,014               5,606,220              3,598,930
    General and administrative                     1,281,895               1,221,605               2,647,196              2,252,666
    Amortization of intangible assets                 37,522                 126,841                  75,043                257,821
                                            -----------------       -----------------        ----------------       ----------------

 Loss from operations                             (2,580,079)             (2,402,314)             (5,338,723)            (4,454,911)

 Other income (expense):
    Other income (expense)                            (1,956)                (34,073)                 58,306                (85,340)
    Interest income                                  271,763                 422,722                 607,177                611,796
    Interest expense                                  (7,141)                (38,387)                (21,087)               (83,836)
                                            -----------------       -----------------        ----------------       ----------------

 Loss from operations before income taxes         (2,317,413)             (2,052,052)             (4,694,327)            (4,012,291)

 Provision for income taxes                           69,604                       -                 133,963                      -
                                            -----------------       -----------------        ----------------       ----------------

 Net loss                                   $     (2,387,017)       $     (2,052,052)        $    (4,828,290)       $    (4,012,291)
                                            =================       =================        ================       ================

 Basic and diluted net loss per share       $          (0.17)       $          (0.15)        $         (0.34)       $         (0.32)
                                            =================       =================        ================       ================

 Weighted average shares outstanding              14,325,153              13,412,271              14,313,335             12,498,771
                                            =================       =================        ================       ================
</TABLE>





                                       2
<PAGE>   5
                               DIGENE CORPORATION
                     CONSOLIDATED STATEMENTS OF CASH FLOWS


<TABLE>
<CAPTION>
                                                                                 SIX MONTHS ENDED
                                                                                   DECEMBER 31,
                                                                      --------------------------------------
                                                                           1998                 1997
                                                                      ---------------       ----------------
                                                                                    (UNAUDITED)
 <S>                                                                  <C>                   <C>
 OPERATING ACTIVITIES
    Net loss                                                          $   (4,828,290)       $    (4,012,291)
    Adjustments to reconcile net loss to net cash used in
       operating activities:
       Depreciation and amortization of property and equipment               778,285                314,009
       Amortization of intangible assets                                      75,042                257,821
       Changes in operating assets and liabilities:
          Accounts receivable                                                216,197                288,407
          Due from related party                                                   -                997,916
          Inventories                                                       (349,257)            (1,157,387)
          Prepaid expenses and other current assets                       (1,326,813)               166,522
          Deposits                                                           (33,946)                44,677
          Accounts payable                                                   124,889               (329,176)
          Accrued expenses                                                   141,951               (222,683)
          Accrued payroll                                                   (139,316)               256,092
          Due to related party                                                     -               (443,332)
          Accrued rent                                                       (23,982)               (22,288)
          Deferred rent                                                      (11,980)               (12,669)
                                                                      ---------------       ----------------

 Net cash used in operating activities                                    (5,377,220)            (3,874,382)

 INVESTING ACTIVITIES
    Purchases of short-term investments                                   (6,186,202)            (5,479,683)
    Maturities of short-term investments                                   1,450,000             10,193,818
    Capital expenditures                                                    (497,387)            (1,125,142)
    Additions to intangible assets                                              (862)                (1,258)
                                                                      ---------------       ----------------

 Net cash provided by (used in) investing activities                      (5,234,451)             3,587,735

 FINANCING ACTIVITIES
      Net proceeds from issuance of Common Stock                                   -             20,654,415
      Exercise of Common Stock options                                        72,432                141,414
      Principal repayments on long-term debt                                (552,717)              (791,012)
                                                                      ---------------       ----------------

 Net cash used in financing activities                                      (480,285)            20,004,817
                                                                      ---------------       ----------------

 Net increase (decrease) in cash and cash equivalents                    (11,091,956)            19,718,170
 Cash and cash equivalents at beginning of period                         18,330,803              8,452,864
                                                                      ---------------       ----------------

 Cash and cash equivalents at end of period                           $    7,238,847        $    28,171,034
                                                                      ===============       ================
</TABLE>





                                       3
<PAGE>   6
                               DIGENE CORPORATION
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


1.  BASIS OF PRESENTATION

The consolidated financial statements for the six month periods ended December
31, 1998 and 1997 are unaudited and include all adjustments which, in the
opinion of management, are necessary to present fairly the results of
operations for the periods then ended.  All such adjustments are of a normal
recurring nature. These consolidated financial statements should be read in
conjunction with the Annual Report on Form 10-K for the year ended June 30,
1998 of Digene Corporation (the "Company"), which includes financial statements
and notes thereto for the years ended June 30, 1998, 1997 and 1996.

The results of the Company's operations for any interim period are not
necessarily indicative of the results of the Company's operations for any other
interim period or for a full fiscal year.

2.  NET LOSS PER SHARE

In 1997, the Financial Accounting Standards Board issued Statement of Financial
Accounting Standards No. 128, "Earnings per Share" ("SFAS No. 128").  SFAS No.
128 replaced the calculation of primary and fully diluted earnings per share
with basic and diluted earnings per share.  Unlike primary earnings per share,
basic earnings per share excludes any dilutive effects of options, warrants,
and convertible securities, except as required by Staff Accounting Bulletin No.
98 ("SAB 98").  The definition of diluted earnings per share is very similar to
the previous definition of fully diluted earnings per share.  All net loss per
share amounts for all periods have been presented, and where appropriate
restated, to conform to the SFAS No. 128 requirements.

3.  ACQUISITION

On July 1, 1998, the Company issued 181,884 shares of its Common Stock, par
value $0.01 per share, as consideration for its purchase of all of the
outstanding capital stock of Viropath B.V., a company with limited liability,
registered at Amsterdam, the Netherlands ("Viropath").  The 181,884 shares of
the Company's Common Stock were recorded at $8.247 per share, in accordance
with the Stock Purchase Agreement, and resulted in total consideration of
approximately $1,500,000.  The Company is obligated to pay royalties on future
sales of Viropath's licensed products, not to exceed $1,000,000.  The
acquisition has been accounted for using the purchase method of accounting.
The Company has allocated the excess of the purchase price over the fair market
value of the acquired net assets as goodwill, which is being amortized on a
straight-line basis over ten years.  The operating results of Viropath are
included in the Company's financial statements since the effective date of the
acquisition. The operating results of Viropath are not considered material to
the consolidated financial statements of the Company, and accordingly, pro
forma financial information has not been presented for this acquisition.





                                       4
<PAGE>   7



ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS

FORWARD LOOKING STATEMENTS.

The following discussion of the financial condition and results of operations
of the Company should be read in conjunction with the Consolidated Financial
Statements and the related Notes thereto included elsewhere in this report and
in the Annual Report on Form 10-K for the year ended June 30, 1998 of Digene
Corporation (the "Company"). Statements that are not statements of historical
fact, and which reflect the intent, belief or expectations of the Company and
its management regarding the anticipated effect of events, circumstances and
trends, should be considered as forward looking statements within the meaning
of the Private Securities Litigation Reform Act of 1995.  Although the Company
believes that its expectations are based on reasonable assumptions within the
bounds of its knowledge of its business and operations, there can be no
assurance that actual results will not differ materially from its expectations.
Factors that might cause or contribute to such differences include, but are not
limited to:  uncertainty of future profitability and cash generation from
operations; uncertainty of clinical trial results for the Company's products
under development; uncertainty of market acceptance of the Company's products
by the worldwide medical community; risks inherent in international
transactions, including those relating to the Company's expansion in Europe,
Brazil and elsewhere; limited sales and marketing experience with a direct
sales force; the extent of future expenditures for sales and marketing
programs; dependence on third-party reimbursement from government entities,
managed care organizations, and private insurance plans; dependence on Abbott
Laboratories as the sole European distributor for the Company's products;
delay in or failure to obtain regulatory approvals for the Company's products
in development; uncertainty regarding patents and proprietary rights in
connection with the Company's products; and the Company's ability to obtain
requisite additional financing to fund the Company's operations beyond fiscal
2000.  Other factors include those set forth under the caption "Additional
Considerations" in the Company's Annual Report on Form 10-K and the documents
referred to therein.

RESULTS OF OPERATIONS

Product sales increased to $3,853,000 and $7,457,000 for the three and six
month periods ended December 31, 1998, respectively, from $2,944,000 and
$5,456,000 for the corresponding periods in 1997.  The increase was due,
primarily, to increased sales of the Company's Hybrid Capture tests, primarily
its HPV test, and equipment, partially offset by lower sales of non-core
products.

Research and development contract revenues increased to $154,000 for the three
and six month periods ended December 31, 1998 from $13,000 and $27,000 for the
corresponding three and six month periods in 1997, respectively.  The increase
was due to the performance of contract research activities, primarily pursuant
to the SBIR contract for HSV research and development, partially offset by
decreases in equipment rental revenues.





                                       5
<PAGE>   8



Cost of product sales increased to $1,429,000 and $2,405,000 for the three and
six month periods ended December 31, 1998, respectively, from $835,000 and
$1,549,000 for the corresponding periods in 1997.  Gross margin on product
sales decreased to 63% and 68% for the three and six month periods ended
December 31, 1998, respectively, from 72% for the corresponding three and six
month periods in 1997, respectively.  The decrease was due, primarily, to
changes in product mix reflecting proportionately greater sales of lower margin
equipment in the 1998 periods than in the 1997 periods.

Research and development expenses were relatively unchanged at $1,185,000 and
$2,217,000 for the three and six month periods ended December 31, 1998,
respectively, compared to $1,288,000 and $2,279,000 for the corresponding
periods in 1997.

Selling and marketing expenses increased to $2,654,000 and $5,606,000 for the
three and six month periods ended December 31, 1998, respectively, from
$1,888,000 and $3,599,000 for the corresponding periods in 1997.  The increase
was due, primarily, to substantial increases in sales and marketing programs
and to the hiring of additional selling and marketing personnel in conjunction
with the Company's efforts to increase product sales.

General and administrative expenses increased to $1,282,000 and $2,647,000 for
the three and six month periods ended December 31, 1998, respectively, from
$1,222,000 and $2,253,000 for the corresponding periods in 1997.  The increase
was due, primarily, to costs associated with the Company's expansion into
markets in Europe.

Interest income decreased to $272,000 and $607,000 for the three and six month
periods ended December 31, 1998, respectively, from $423,000 and $612,000 for
the corresponding periods in 1997.  The decrease was due to a decrease in the
Company's cash, cash equivalents and short-term investments as a result of the
Company's continuing negative cash flows, partially offset by the receipt of
the net proceeds from the public offering of 2,250,000 shares of the Company's
common stock in October 1997.

LIQUIDITY AND CAPITAL RESOURCES

Since inception, the Company's expenses have significantly exceeded its
revenues, resulting in accumulated deficit of approximately $44,244,000 at
December 31, 1998.  The Company has funded its operations primarily through the
sale of equity securities.  The Company experienced negative cash flows from
operations of $5,377,000 and $3,874,000 for the six months ended December 31,
1998, and 1997, respectively.

Capital expenditures decreased to $497,000 for the six months ended December
31, 1998 from $1,125,000 for the corresponding period in 1997, due, primarily,
to less expenditure related to equipment placements.

The Company does not have any bank financing arrangements.





                                       6
<PAGE>   9



On October 20, 1997, the Company completed a public offering of 2,250,000
shares of its common stock, the net proceeds of which, after underwriters'
commissions and expenses, were $20,654,000.

The Company has incurred negative cash flows from operations since its
inception, and has expended, and expects to continue to expend in the future,
substantial funds to complete its planned product development efforts, expand
its sales and marketing activities and expand its manufacturing capabilities.
The Company expects that its existing capital resources will be adequate to
fund the Company's operations through fiscal 2000. No assurances can be given
that there will be no changes in the Company that would consume a significant
amount of its available resources before that time.  The Company's future
capital requirements and the adequacy of available funds will depend on
numerous factors, including the successful commercialization of its products,
progress in its product development efforts and the magnitude and scope of such
efforts, progress with preclinical studies and clinical trials, progress in its
regulatory affairs activities, the cost and timing of expansion of
manufacturing capabilities, the expansion of the Company's direct European
sales operations, the development and maintenance of effective sales and
marketing activities, the cost of filing, prosecuting, defending and enforcing
patent claims and other intellectual property rights, competing technological
and market developments, and the development of strategic alliances for the
marketing of its products.  To the extent that the Company's existing capital
resources and funds generated from the Company's operations, if any, are
insufficient to meet current or planned operating requirements, the Company
will be required to obtain additional funds through equity or debt financing,
strategic alliances with corporate partners and others, or through other
sources. The Company does not have any committed sources of additional
financing, and there can be no assurance that additional funding, if necessary,
will be available on acceptable terms, if at all. If adequate funds are not
available, the Company may be required to delay, scale back or eliminate
certain aspects of its operations or attempt to obtain funds through
arrangements with collaborative partners or others that may require the Company
to relinquish rights to certain of its technologies, product candidates,
products or potential markets.  If adequate funds are not available, the
Company's business, financial condition and results of operations will be
materially and adversely effected.





                                       7
<PAGE>   10



YEAR 2000 COMPLIANCE

The Company is working to resolve the potential impact of the year 2000 on the
ability of the Company's computerized information programs and systems and
certain manufacturing and other equipment to accurately process information
that may be date-sensitive.  Any of the Company's technology that recognizes a
date using "00" as the year 1900 rather than the year 2000 could result in
errors or system failures.

The Company has substantially completed an assessment of its computer programs
and telephone systems and has identified those programs and systems that are
presently not year 2000 compliant. The Company is in the process of assessing
its manufacturing and other equipment, as well as communicating with
significant vendors or customers to determine their respective states of
readiness.  The Company expects to complete this assessment in the first
quarter of calendar 1999.

In connection with the planned relocation of the Company's business to a new
facility in Gaithersburg, Maryland in December 1999, the Company expects to
replace most of its programs, systems and manufacturing and other equipment
with new programs, systems and equipment which the suppliers will certify to be
year 2000 compliant.  By the summer of 1999 the Company plans to upgrade, to    
the extent necessary, any of its existing mission critical programs, systems
and equipment that will be transferred to the new facility.  If the relocation
is significantly delayed, which the Company does not presently anticipate, the
Company expects to expand the upgrade and replacement phase to include the
necessary upgrade and replacement of programs, systems and equipment which are
located at its existing facilities but which the Company does not plan to use
at the new facility.  The cost of these contingent upgrades and replacements is
presently unknown.

The Company is in the process of testing upgraded or replaced programs, systems
and equipment and will continue the testing phase throughout calendar 1999.
Based on information developed to date as a result of its assessment efforts,
the Company does not anticipate that the cost of upgrading or replacing its
programs, systems and equipment for the purpose of making them year 2000        
compliant will be material to the Company. If the Company and third parties
upon which it relies are unable to address the year 2000 issue in a timely and
successful manner, the Company's business could be materially adversely
affected.





                                       8
<PAGE>   11



Item 6.  Exhibits and Reports on Form 8-K

(a)  Exhibits

3.1   Amended and Restated Certificate of Incorporation (Incorporated by
      reference to Exhibit 3.1 to the Company's Registration Statement on Form
      S-1 (File No. 333-2968))

3.2   Amended and Restated Bylaws (Incorporated by reference to Exhibit 3.2 to
      the Company's Registration Statement on Form S-1 (File No. 333-2968))

4.1   Form of Common Stock Certificate (Incorporated by reference to Exhibit
      4.1 to the Company's Registration Statement on Form S-1 (File No.
      333-2968))

10.1  Employment Agreement for Jeanmarie P. Curley dated December 22, 1998

10.2  Employment Agreement for Joseph P. Slattery dated December 22, 1998

27    Financial Data Schedule

(b) Reports on Form 8-K

The Company did not file any reports on Form 8-K during the quarter ended
December 31, 1998.





                                       9
<PAGE>   12



                                   SIGNATURES

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.

                                
                                                   DIGENE CORPORATION          
                                
                                
Date:     February 10, 1999          By:  /s/  Charles M. Fleischman           
     ---------------------------        ---------------------------------------
                                               Charles M. Fleischman
                                               Executive Vice President,
                                              Chief Operating Officer and
                                                Chief Financial Officer
                                             (Principal Financial Officer)
                                
Date:     February 10, 1999         By:  /s/  Joseph P. Slattery              
     ---------------------------       -----------------------------------------
                                              Joseph P. Slattery
                                        Vice President, Finance and Controller
                                            (Principal Accounting Officer)





                                       10
<PAGE>   13



                                 EXHIBIT INDEX



<TABLE>
<CAPTION>
   Exhibit No.            Description                                                   Page
   -----------            -----------                                                   ----
       <S>                <C>
       3.1                Amended and Restated Certificate of Incorporation
                          (Incorporated by reference to Exhibit 3.1 to the
                          Company's Registration Statement on Form S-1 (File
                          No. 333-2968))

       3.2                Amended and Restated Bylaws (Incorporated by
                          reference to Exhibit 3.2 to the Company's
                          Registration Statement on Form S-1 (File No.
                          333-2968))

       4.1                Form of Common Stock Certificate (Incorporated by
                          reference to Exhibit 4.1 to the Company's
                          Registration Statement on Form S-1 (File No.
                          333-2968))

       10.1               Employment Agreement for Jeanmarie P. Curley dated
                          December 22, 1998

       10.2               Employment Agreement for Joseph P. Slattery dated
                          December 22, 1998

        27                Financial Data Schedule
</TABLE>





                                       11