<PAGE>
 
                                                                     Exhibit 3.1
 
                             AMENDED AND RESTATED
                         CERTIFICATE OF INCORPORATION

                                      OF

                              MMC NETWORKS, INC.



MMC Networks, a corporation organized and existing under the laws of the State
of Delaware, does hereby certify:

     1.   The name of the corporation is MMC Networks, Inc.  MMC Networks, Inc.
was originally incorporated under the same name, and the original Certificate of
Incorporation was filed with the Secretary of State of the State of Delaware on
August 11, 1997.

     2.   Pursuant to Sections 242 and 228 of the General Corporation Law of the
State of Delaware, the amendments and restatement herein set forth have been
duly approved by the Board of Directors and stockholders of MMC Networks, Inc.

     3.   Pursuant to Section 245 of the General Corporation Law of the State of
Delaware, this Amended and Restated Certificate of Incorporation restates and
integrates and amends the provisions of the Certificate of Incorporation of this
corporation.

     4.   The text of the Restated Certificate of Incorporation as is hereby
restated and amended to read in its entirety as follows:

                                     FIRST

     The name of the Corporation is MMC Networks, Inc. (the "Corporation").

                                     SECOND

     The address of the Corporation's registered office in the State of Delaware
is 1013 Centre Road, Wilmington, County of New Castle, Delaware 19805.  The name
of its registered agent at such address is Corporation Service Company.

                                     THIRD

     The purpose of the Corporation is to engage in any lawful act or activity
for which corporations may be organized under the General Corporation Law of
Delaware.
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                                     FOURTH

     A.   The total number of shares which the Corporation shall have authority
to issue is 110,000,000 shares of capital stock.

     B.   Of such authorized shares, one hundred million (100,000,000) shares
shall be designated "Common Stock", and have a par value of $.001.

     C.   Of such authorized shares, ten million (10,000,000) shares shall be
designated "Preferred Stock", and have a par value of $.001.  The Preferred
Stock may be issued from time to time in one or more series.  The Board of
Directors of the Corporation is authorized to determine or alter the powers,
preferences and rights and the qualifications, limitations or restrictions
granted to or imposed upon any wholly unissued series of Preferred Stock, and
within the limitations or restrictions stated in any resolution or resolutions
of the Board of Directors originally fixing the number of shares constituting
any series, to increase or decrease (but not below the number of shares of any
such series then outstanding) the number of shares of any such series subsequent
to the issuance of shares of that series, to determine the designation of any
series, and to fix the number of shares of any series.  In case the number of
shares of any series shall be so decreased, the shares constituting such
decrease shall resume the status which they had prior to the adoption of the
resolution originally fixing the number of shares of such series.

                                     FIFTH
                                        
     The Corporation is to have perpetual existence.

                                     SIXTH

     Elections of directors need not be by written ballot unless a stockholder
demands election by written ballot at the meeting and before voting begins.

                                    SEVENTH

     The number of directors which constitute the whole Board of Directors of
the Corporation shall be designated in the Bylaws of the Corporation.

                                     EIGHTH

     In furtherance and not in limitation of the powers conferred by statute,
the Board of Directors is expressly authorized to make, alter, amend or repeal
the Bylaws of the Corporation.

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                                     NINTH

     To the fullest extent permitted by the Delaware General Corporation Law as
the same exists or as it may hereafter be amended, no director of the
Corporation shall be personally liable to the Corporation or its stockholders
for monetary damages for breach of fiduciary duty as a director.

     Neither any amendment nor repeal of this Article, nor the adoption of any
provision of this Restated Certificate of Incorporation inconsistent with this
Article, shall eliminate or reduce the effect of this Article in respect of any
matter occurring, or any cause of action, suit or claim that, but for this
Article, would accrue or arise, prior to such amendment, repeal or adoption of
an inconsistent provision.

                                     TENTH

     Section 1.  At each annual meeting of stockholders, directors of the
Corporation shall be elected to hold office until the expiration of the term for
which they are elected, and until their successors have been duly elected and
qualified; except that if any such election shall be not so held, such election
shall take place at stockholders' meeting called and held in accordance with the
Delaware General Corporation Law.  The directors of the Corporation shall be
divided into three classes as nearly equal in size as is practicable, hereby
designed Class I, Class II and Class III.  The term of office of the initial
Class I directors shall expire at the next succeeding annual meeting of
stockholders, the term of  office of the initial Class II directors shall expire
at the second succeeding annual meeting of stockholders and the term of office
of the initial Class III directors shall expire at the third succeeding annual
meeting of the stockholders.  For the purposes hereof, the initial Class I,
Class II and Class III directors shall be those directors so designated by the
incorporator.  At each annual meeting of stockholders, directors to replace
those of a Class whose terms expire at such annual meeting shall be elected to
hold office until the third succeeding annual meeting and until their respective
successors shall have been duly elected and qualified.  If the number of
directors is hereafter changed, any newly created directorships or decrease in
directorships shall be so apportioned among the classes as to make all classes
as nearly equal in number as if practicable.

     Section 2.  The number of directors which constitute the whole Board of
Directors of the Corporation shall be designated in the Bylaws of the
Corporation.

     Section 3.  Vacancies occurring on the Board of Directors for any reason
may be filled by vote of a majority of the remaining members of the Board of
Directors, although less than a quorum, at any meeting of the Board of
Directors.  A person so elected by the Board of Directors to fill a vacancy
shall hold office until the next succeeding annual meeting of stockholders of
the Corporation and until his or her successor shall have been duly elected and
qualified.

                                    ELEVENTH

     Meetings of stockholders may be held within or without the State of
Delaware, as the Bylaws may provide.  The books of the Corporation may be kept
(subject to any provision contained in the 

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statutes) outside of the State of Delaware at such place or places as may be
designated from time to time by the Board of Directors or in the Bylaws of the
Corporation.

                                    TWELFTH

     The stockholders of the Corporation may not take action by written consent
in lieu of a meeting but must take any actions at a duly called annual or
special meeting.

                                   THIRTEENTH

     Notwithstanding any other provisions of this Restated Certificate of
Incorporation or any provision of law which might otherwise permit a lesser vote
or no vote, but in addition to any affirmative vote of the holders of the
capital stock required by law or this Restated Certificate of Incorporation, the
affirmative vote of the holders of at least two-thirds (2/3) of the combined
voting power of all of the then outstanding shares of the Corporation entitled
to vote shall be required to alter, amend or repeal Articles TENTH, TWELFTH or
THIRTEENTH or any provision thereof, unless such amendment shall be approved by
a majority of the directors of the Corporation not affiliated or associated with
any person or entity holding (or which has announced an intention to obtain) 20%
or more of the voting power of the Corporation's outstanding capital stock.

                                   FOURTEENTH

     The Corporation reserves the right to amend, alter, change or repeal any
provision contained in this Certificate of Incorporation, in the manner now or
hereafter prescribed by statute, and all rights conferred upon stockholders
herein are granted subject to this reservation.

     IN WITNESS WHEREOF, MMC Networks, Inc., has caused this Amended and
Restated Certificate of Incorporation to be executed by Prabhat K. Dubey, its
President and Chief Executive Officer attested by Amos Wilnai, its Chairman and
Executive Vice President, this 5th day of November, 1997.


                                        /s/ PRABHAT K. DUBEY
                                        -------------------------------------
                                        Prabhat K. Dubey
                                        President and Chief Executive Officer

ATTEST


/s/ AMOS WILNAI
-------------------------------------
Amos Wilnai
Chairman of the Board and
Executive Vice President

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