<PAGE>   1
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                                  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 March 31, 1999

                                       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)

                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)


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.

                                                   Shares outstanding as of
                 Class                                   May 13, 1999
--------------------------------------                 -----------------
Common Stock, par value $.01 per share                    14,421,421
================================================================================
<PAGE>   2
                               DIGENE CORPORATION

                               INDEX TO FORM 10-Q

                                                                            Page
                                                                            ----
PART I.  CONSOLIDATED FINANCIAL INFORMATION:

         Item 1.  Consolidated Financial Statements -

                  Consolidated Balance Sheets -
                      March 31, 1999 and June 30, 1998                         1

                  Consolidated Statements of Operations -
                      Three months ended March 31, 1999 and 1998;
                      Nine months ended March 31, 1999 and 1998;               2

                  Consolidated Statements of Cash Flows -
                      Nine months ended March 31, 1999 and 1998                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
<PAGE>   3
PART I.  CONSOLIDATED FINANCIAL INFORMATION

ITEM 1.

                               DIGENE CORPORATION
                           CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                                      MARCH 31,                 JUNE 30,
                                                                                         1999                     1998
                                                                                 ---------------------     --------------------
                                                                                     (UNAUDITED)

<S>                                                                              <C>                      <C>
                                     ASSETS
Current assets:
     Cash and cash equivalents                                                   $       11,392,006        $      18,330,803
     Short-term investments                                                               4,409,814                7,181,572
     Accounts receivable, less allowance of approximately $209,000 at
         March 31, 1999 and June 30, 1998, respectively                                   4,834,933                3,072,224
     Inventories                                                                          3,177,519                3,557,289
     Prepaid expenses and other current assets                                            1,762,980                  560,706
                                                                                 ---------------------     --------------------
Total current assets                                                                     25,577,252               32,702,594

Property and equipment, net                                                               2,151,576                2,627,244
Intangible assets, net                                                                    1,396,529                   12,784
Deposits                                                                                    127,732                   96,916
                                                                                 ---------------------     --------------------

Total assets                                                                     $       29,253,089        $      35,439,538
                                                                                 =====================     ====================

                      LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:
     Accounts payable                                                            $        1,588,587        $       2,424,245
     Accrued expenses                                                                       684,849                  542,064
     Accrued payroll                                                                        811,925                  755,490
     Current maturities of long-term debt                                                     1,002                  552,717
                                                                                 ---------------------     --------------------

Total current liabilities                                                                 3,086,363                4,274,516

Accrued rent                                                                                 22,124                   54,340
Deferred rent                                                                                     -                   11,980

Stockholders' equity:
     Common stock, $.01 par value, 50,000,000 shares authorized, 14,362,521
         and 14,117,308 shares issued and outstanding at March 31, 1999
         and June 30, 1998, respectively                                                    143,625                  141,173
     Additional paid-in capital                                                          71,980,264               70,373,310
     Accumulated deficit                                                                (45,979,287)             (39,415,781)
                                                                                 ---------------------     --------------------

Total stockholders' equity                                                               26,144,602               31,098,702
                                                                                 ---------------------     --------------------

Total liabilities and stockholders' equity                                       $       29,253,089        $      35,439,538
                                                                                 =====================     ====================

</TABLE>

                                       1
<PAGE>   4
                               DIGENE CORPORATION
                      CONSOLIDATED STATEMENTS OF OPERATIONS
                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                     THREE MONTHS ENDED                               NINE MONTHS ENDED
                                                          MARCH 31,                                       MARCH 31,
                                           ----------------------------------------      -------------------------------------
                                                  1999                 1998                     1999               1998
                                           -------------------   ------------------      -----------------   -----------------


<S>                                        <C>                   <C>                     <C>                 <C>
Revenues:
     Product sales                         $      4,634,602      $     3,231,388         $   12,091,578      $    8,687,625
     Research and development contracts             156,754                    -                310,615              26,500
                                           -------------------   ------------------      -----------------   -----------------

Total revenues                                    4,791,356            3,231,388             12,402,193           8,714,125

Costs and expenses:
     Cost of product sales                        1,695,700              970,594              4,100,255           2,519,843
     Research and development                     1,291,693            1,518,899              3,508,239           3,797,881
     Selling and marketing                        2,343,533            2,996,807              7,949,753           6,595,737
     General and administrative                   1,161,548            1,354,211              3,808,744           3,606,877
     Amortization of intangible assets               37,522              125,192                112,565             383,013
                                           -------------------   ------------------      -----------------   -----------------

Loss from operations                             (1,738,640)          (3,734,315)            (7,077,363)         (8,189,226)

Other income (expense):
     Other income (expense)                        (235,551)             (58,999)              (177,245)           (144,339)
     Interest income                                225,049              416,497                832,226           1,028,293
     Interest expense                                     -              (34,728)               (21,087)           (118,564)
                                           -------------------   ------------------      -----------------   -----------------


Loss from operations before income taxes         (1,749,142)          (3,411,545)            (6,443,469)         (7,423,836)

Provision (benefit) for income taxes                (13,926)                   -                120,037                   -
                                           -------------------   ------------------      -----------------   -----------------

Net loss                                   $     (1,735,216)     $    (3,411,545)        $   (6,563,506)     $   (7,423,836)
                                           ===================   ==================      =================   =================

Basic and diluted net loss per share       $          (0.12)     $         (0.25)        $        (0.46)     $        (0.57)
                                           ===================   ==================      =================   =================


Weighted average shares outstanding              14,334,094           13,908,214             14,320,153          12,961,727
                                           ===================   ==================      =================   =================
</TABLE>

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

<TABLE>
<CAPTION>
                                                                                       NINE MONTHS ENDED
                                                                                           MARCH 31,
                                                                         ----------------------------------------------
                                                                                 1999                     1998
                                                                         ---------------------     --------------------
                                                                                          (UNAUDITED)
<S>                                                                      <C>                      <C>
OPERATING ACTIVITIES
     Net loss                                                            $       (6,563,506)       $      (7,423,836)
     Adjustments to reconcile net loss to net cash used in
         operating activities:
         Depreciation and amortization of property and equipment                  1,089,911                  553,183
         Amortization of intangible assets                                          117,114                  383,014
         Changes in operating assets and liabilities:
              Accounts receivable                                                (1,762,709)                  90,371
              Due from related party                                                      -                  843,459
              Inventories                                                           379,770               (1,693,084)
              Prepaid expenses and other current assets                          (1,202,274)                 144,006
              Deposits                                                              (30,816)                  26,470
              Accounts payable                                                     (835,658)                (265,721)
              Accrued expenses                                                      142,785                 (122,546)
              Accrued payroll                                                        56,435                  531,766
              Due to related party                                                        -                 (443,332)
              Accrued rent                                                          (32,216)                 (34,287)
              Deferred rent                                                         (11,980)                 (19,004)
                                                                         ---------------------     ---------------------

Net cash used in operating activities                                            (8,653,144)              (7,429,541)

INVESTING ACTIVITIES
     Purchases of short-term investments                                         (6,186,202)             (11,496,883)
     Maturities of short-term investments                                         8,957,960               11,242,792
     Capital expenditures                                                          (614,243)              (1,874,179)
     Additions to intangible assets                                                    (862)                  (4,323)
                                                                         ---------------------     ---------------------

Net cash provided by (used in) investing activities                               2,156,653               (2,132,593)

FINANCING ACTIVITIES
     Net proceeds from issuance of Common Stock                                           -               20,654,415
     Exercise of Common Stock options                                               109,409                  194,361
     Principal repayments on long-term debt                                        (551,715)                (723,269)
                                                                         ---------------------     ---------------------

Net cash used in financing activities                                              (442,306)              20,125,507
                                                                         ---------------------     ---------------------

Net increase (decrease) in cash and cash equivalents                             (6,938,797)              10,563,373
Cash and cash equivalents at beginning of period                                 18,330,803                8,452,864
                                                                         ---------------------     ---------------------

Cash and cash equivalents at end of period                               $       11,392,006        $      19,016,237
                                                                         =====================     =====================
</TABLE>

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

1. BASIS OF PRESENTATION

The consolidated financial statements for the nine month periods ended March 31,
1999 and 1998 are unaudited and include all adjustments which, in the opinion of
management, are necessary to present fairly the financial position and results
of operations for the periods then ended. All such adjustments are of a normal
recurring nature. These unaudited consolidated financial statements should be
read in conjunction with the financial statements and notes thereto included in
the Company's Annual Report on Form 10-K for the year ended June 30, 1998 filed
with the Securities and Exchange Commission.

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 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 Company's Annual Report on Form 10-K for the year ended June 30, 1998.
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 principal
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 $4,635,000 and $12,092,000 for the three and nine
month periods ended March 31, 1999, respectively, from $3,231,000 and $8,688,000
for the corresponding periods in 1998. The increase was due, primarily, to
increased sales volume with respect to 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 $157,000 and $311,000
for the three and nine month periods ended March 31, 1999, respectively, from $0
and $27,000 for the corresponding periods in 1998. The increase was due to the
performance of contract research activities, primarily pursuant to a SBIR
contract for HSV research and development.


                                       5
<PAGE>   8
Cost of product sales increased to $1,696,000 and $4,100,000 for the three and
nine month periods ended March 31, 1999, respectively, from $971,000 and
$2,520,000 for the corresponding periods in 1998 due to increased volume of
products sold. Gross margin on product sales decreased to 63% and 66% for the
three and nine month periods ended March 31, 1999, respectively, from 70% and
71% for the corresponding periods in 1998. The percentage decrease was due,
primarily, to changes in product mix reflecting proportionately greater sales
of lower margin equipment in the 1999 periods than in the 1998 periods.

Research and development expenses decreased to $1,292,000 and $3,508,000 for the
three and nine month periods ended March 31, 1999, respectively, compared to
$1,519,000 and $3,798,000 for the corresponding periods in 1998. The decrease
was due, primarily, to a reduction in spending for external professional
services related to certain research and development programs, partially offset
by the hiring of additional personnel.

Selling and marketing expenses decreased to $2,344,000 and increased to
$7,950,000 for the three and nine month periods ended March 31, 1999,
respectively, from $2,997,000 and $6,596,000 for the corresponding periods in
1998. The decrease in the three month period was due, primarily, to a reduction
in spending for marketing conferences. The increase in the nine month period 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 decreased to $1,162,000 and increased to
$3,809,000 for the three and nine month periods ended March 31, 1999,
respectively, from $1,354,000 and $3,607,000 for the corresponding periods in
1998. The decrease in the three month period was due, primarily, to a decrease
in spending on professional services. The increase in the nine month period was
due, primarily, to costs associated with the Company's expansion into markets in
Europe.

Interest income decreased to $225,000 and $832,000 for the three and nine month
periods ended March 31, 1999, respectively, from $416,000 and $1,028,000 for the
corresponding periods in 1998. 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.

LIQUIDITY AND CAPITAL RESOURCES

Since inception, the Company's expenses have significantly exceeded its
revenues, resulting in an accumulated deficit of approximately $45,979,000 at
March 31, 1999. The Company has funded its operations primarily through the
sale of equity securities. The Company experienced negative cash flows from
operations of $8,653,000 and $7,430,000 for the nine months ended March 31,
1999, and 1998, respectively.


                                       6
<PAGE>   9
Capital expenditures decreased to $614,000 for the nine months ended March 31,
1999 from $1,874,000 for the corresponding period in 1998, due, primarily, to
reduced equipment placements at the Company's expense.

The Company does not have any bank financing arrangements.

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
additional 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 the Company's
products, the degree of success of Abbott Laboratories in distributing the
Company's products in Europe, progress in the Company's product development
efforts and the magnitude and scope of such efforts, progress with preclinical
studies and clinical trials, progress in the Company's regulatory affairs
activities, the cost and timing of expansion of manufacturing capabilities, the
expansion of the Company's European marketing 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 READINESS DISCLOSURE

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. All programs and systems that management
considers "mission critical" have been assessed and, in many cases, have already
been upgraded and tested. 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 by July, 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, all 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 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))

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 March
31, 1999.


                                       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:          May 14, 1999                   By:  /s/  Charles M. Fleischman
     --------------------------------            ----------------------------
                                                     Charles M. Fleischman
                                                   Executive Vice President,
                                                  Chief Operating Officer and
                                                    Chief Financial Officer
                                                 (Principal Financial Officer)

Date:          May 14, 1999                   By:  /s/  Joseph P. Slattery
     -------------------------------             -----------------------------
                                                       Joseph P. Slattery
                                                     Vice President, Finance
                                                         and Controller
                                                 (Principal Accounting Officer)


                                       10
<PAGE>   13
                                  EXHIBIT INDEX


 Exhibit No.     Description                                               Page
 -----------     -----------                                               ----

    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))

    27           Financial Data Schedule


                                       11