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

                                   FORM 10-K/A

                (Mark One)

            [X] ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934
                   For the fiscal year ended December 31, 1998

                                       OR

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

                         Commission file number: 0-12042

                                  BIOGEN, INC.
             (Exact name of Registrant as specified in its charter)


          Massachusetts                                          04-3002117
  (State or other jurisdiction                                (I.R.S. Employer
of incorporation or organization)                            Identification No.)


               14 Cambridge Center, Cambridge, Massachusetts 02142
               (Address of principal executive offices)(zip code)

       Registrant's telephone number, including area code: (617) 679-2000

        Securities registered pursuant to Section 12(b) of the Act: None

    Securities registered pursuant to Section 12(g) of the Act: Common Stock,
                                 $.01 par value
                                (Title of class)

         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 by check mark if disclosure of delinquent filers pursuant to
Item 405 of Regulation S-K is not contained herein, and will not be contained,
to the best of Registrant's knowledge, in definitive proxy or information
statements incorporated by reference in Part III of this Form 10-K or any
amendment to this Form 10-K. [ ]

         Aggregate market value of Common Stock held by nonaffiliates of the
Registrant at March 9, 1999 (excludes shares held by directors): $8,018,804,742.
Exclusion of shares held by any person should not be construed to indicate that
such person possesses the power, direct or indirect, to direct or cause the
direction of management or policies of the Registrant, or that such person is
controlled by or under common control with the Registrant. Common Stock
outstanding at March 9, 1999: 75,111,450 shares.

                       DOCUMENTS INCORPORATED BY REFERENCE

         Portions of the Registrant's 1998 Annual Report to Shareholders are
incorporated by reference into Parts II and IV of this Report.
<PAGE>   2
         This Form 10-K/A amends the Company's Annual Report on Form 10-K for
the fiscal year ended December 31, 1998 to add as exhibits to the Form 10-K the
financial statements for the Biogen Savings Plan and the related independent
accountants' consent.
<PAGE>   3
PART IV

ITEM 14.  EXHIBITS, FINANCIAL STATEMENT SCHEDULES, AND REPORTS ON FORM 8-K

         (3) Exhibits

The following documents are added as exhibits to the Form 10-K:

Exhibit No.    Description

(23)           Consent of PricewaterhouseCoopers LLP

(99.1)         Financial Statements for Biogen Savings Plan
<PAGE>   4
         Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Registrant has duly caused this report to be signed on
its behalf by the undersigned, thereunto duly authorized.

BIOGEN, INC.


By: /s/ Michael J. Astrue
    ----------------------------------------
    Michael J. Astrue
    Vice President - General Counsel

Dated  June 28, 1999