<PAGE>

                                                                     Exhibit 4.1
                                                                     -----------

THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS
AMENDED.  THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE
ABSENCE OF A REGISTRATION STATEMENT IN EFFECT WITH RESPECT TO THE SECURITIES
UNDER SUCH ACT OR AN EXEMPTION FROM SUCH REQUIREMENT UNDER SUCH ACT.


                                                                 37,402 Warrants

No. 001

                        CONTROL DELIVERY SYSTEMS, INC.
                       COMMON STOCK WARRANT CERTIFICATE


                         DEUTSCHE BANK SECURITIES INC.

          THIS CERTIFIES that, for valued received, Deutsche Bank Securities
Inc., or its registered successors and assigns (the "Warrant Holder"), is the
                                                     --------------
owner of the number of warrants (the "Warrants") set forth above, each to
                                      --------
purchase from Control Delivery Systems, Inc., a Delaware corporation (the
"Company"), at any time or from time to time but in any event no later than the
earlier to occur of (a) April 7, 2002 or (b) the date one year following the
closing of the Company's initial public offering of its Common Stock ("Common
                                                                       ------
Stock"), par value $0.01 per share (the "Expiration Date"), one share of Common
-----                                    ---------------
Stock at an initial exercise price of $53.74, subject to adjustment from time to
time pursuant to the provisions of Section 2 hereof.  For purposes of this
Warrant Certificate, the term "Common Shares" shall mean the class of capital
                               -------------
stock of the Company designated Common Stock, par value $0.01, pursuant to the
Company's Certificate of Incorporation, as amended, and any other class of
capital stock of the Company resulting from successive changes or
reclassification of the Common Stock.

          1.   Exercise of Warrants. The Warrants evidenced hereby may be
               --------------------
     exercised at any time through the Expiration Date by the registered holder
     hereof, in whole or in part, by (a) the surrender of this Warrant
     Certificate, duly endorsed (unless endorsement is waived by the Company),
     at the principal office of the Company (or at such other office or agency
     of the Company as it may designate by notice in writing to the registered
     holder hereof at such holder's last address appearing on the books of the
     Company), (b) the delivery of a completed and executed Notice of Exercise
     in the form of Exhibit A and (c) upon payment of the aggregate Exercise
                    ---------
     Price (as defined below) of the Common Shares purchased. The certificate(s)
     for such Common Shares shall be delivered to the registered holder hereof
     within a reasonable time after Warrants evidenced hereby shall have been so
     exercised and a new Warrant Certificate evidencing the number of Warrants,
     if any, remaining unexercised shall also be issued to the registered holder
     within such time unless such Warrants have expired. No fractional Common
     Shares of the Company, or scrips for any such fractional shares, shall be
     issued upon the exercise of any Warrants; but the holder

                                       1
<PAGE>

hereof shall be entitled to cash equal to such fraction multiplied by the Market
Price on the date of exercise.

If the Market Price of a share of Common Stock exceeds the Exercise Price on the
business day immediately prior to the exercise of the Warrant, the registered
holder may exercise the Warrants held by such holder, without the payment of any
additional consideration, for a number of shares of Common Stock determined by
dividing (i) the result of the difference between such Market Price and the
Exercise Price times the number of shares of Common Stock into which the
Warrants held by such Holder are exercisable, by (ii) such Market Price. No
fractional shares will be issued, and the Company will pay the registered holder
in cash for any such fractional share otherwise issuable. The Market Price for
any day shall be the last reported sale price regular way or, in case no such
reported sale takes place on such day, the average of the closing bid and asked
prices regular way for such day, in each case (1) on the principal national
securities exchange on which the shares of Common Stock are listed or to which
such shares are admitted to trading or (2) if the Common Stock is not listed or
admitted to trading on a national securities exchange, in the over-the-counter
market as reported by NASDAQ or any comparable system or (3) if the Common Stock
is not listed on NASDAQ or a comparable system, or if for any other reason the
Market Price cannot be determined pursuant to the foregoing provisions, as
determined in good faith by the Board of Directors of the Company.

     2.  Adjustment in Exercise Price and Number of Shares. The initial exercise
price of $53.74 per share shall be subject to adjustment from time to time as
hereinafter provided (such initial exercise price, as last adjusted, the
"Exercise Price"). Upon each adjustment of the Exercise Price, the holder of
this Warrant Certificate shall thereafter be entitled to purchase at the
Exercise Price resulting from such adjustment, the number of shares obtained by
dividing (a) the product of (x) the number of Common Shares purchasable pursuant
hereto immediately prior to such adjustment and (y) the Exercise Price
immediately preceding such adjustment by (b) the Exercise Price resulting from
such adjustment.

         (a)   Subdivision or Combination of Stock. If and whenever the Company
     shall at any time subdivide its outstanding Common Shares into a greater
     number of shares, the Exercise Price in effect immediately prior to such
     subdivision shall be proportionately reduced, and conversely, in case the
     outstanding Common Shares of the Company shall be combined into a smaller
     number of shares, the Exercise Price in effect immediately prior to such
     combination shall be proportionately increased.

         (b)   Stock Dividends. If and whenever at any time the Company shall
     declare a dividend or make any other distribution upon any class or series
     of stock of the Company payable in Common Shares, the Exercise Price in
     effect immediately prior to such dividend or distribution shall be
     proportionately reduced as if such dividend or distribution had been made
     by way of a subdivision pursuant to Section 2(a) above.

                                       2
<PAGE>

          (c)  Reorganization, Reclassification, Consolidation, Merger. If any
               -------------------------------------------------------
     capital reorganization, reclassification of the capital stock of the
     Company, consolidation or merger of the Company with another corporation,
     or sale, transfer or other disposition of all or substantially all of the
     Company's properties to another corporation shall be effected, then, lawful
     and adequate provision shall be made whereby each holder of Warrants shall
     thereafter have the right to purchase and receive upon the basis and upon
     the terms and conditions herein specified and in lieu of the Common Shares
     immediately theretofore issuable upon exercise or the Warrants, such shares
     of stock, securities or properties (including cash paid as partial
     consideration) (collectively, the "Substitute Securities") as may be
     issuable or payable with respect to or in exchange for a number of
     outstanding Common Shares equal to the number of Common Shares issuable
     upon exercise of the Warrants immediately prior to such reorganization,
     reclassification, consolidation, merger, sale, transfer or other
     disposition, and in any such case, appropriate provision shall be made with
     respect to the rights and interests of each holder of Warrants to the end
     that the provisions hereof shall thereafter be applicable, as nearly
     equivalent as may be practicable in relation to any Substitute Securities
     thereafter deliverable upon the exercise thereof. The above provisions of
     this Subsection 2(c) shall similarly apply to successive reorganizations,
     reclassification, consolidations, mergers, sales, transfers or
     dispositions.

     3.  Company to Provide Stock. The Company covenants and agrees that all the
         ------------------------
Common Shares which may be issued upon the exercise of the Warrants evidenced
hereby upon the due exercise, including the receipt by the Company of the
aggregate Exercise Price for all Warrants exercised, will be duly authorized,
validly issued and fully paid and nonassessable and free from all taxes, liens
and charges with respect to the issue thereof to the registered holder hereof
other than those which the Company shall promptly pay or discharge. The Company
further covenants and agrees that during the period within which the Warrants
evidenced hereby may be exercised, the Company will at all times reserve such
number of Common Shares as may be sufficient to permit the exercise in full of
the Warrants hereby.

     4.  Representations and Warranties of the Warrant Holder. The Warrant
         ----------------------------------------------------
Holder hereby represents and warrants to the Company as follows:

         (a)   Purchase For Own Account.  The Warrants issued to the Warrant
               ------------------------
     Holder pursuant to this Warrant Certificate, and the Common Shares to be
     issued upon exercise thereof, are being or will be acquired for the Warrant
     Holder's own account and with no intention of distributing or reselling
     such securities or any part thereof in any transaction that would be in
     violation of the securities laws of the United States.

         (b)   Restricted Securities.  The Warrant Holder understands that the
               ---------------------
     Warrants are not, and the Common Shares issuable upon exercise of the
     Warrants will not be, registered at the time of their issuance under the
     Securities Act for the reason that the sale provided for in this Warrant
     Certificate is exempt pursuant to Section 4(2) of the Securities Act and
     that reliance of the Company on such exemption is predicated in

                                       3
<PAGE>

     part on such Warrant Holder's representations set forth herein. The Warrant
     Holder represents that it is experienced in evaluating companies such as
     the Company, has such knowledge and experience in financial and business
     matters as to be capable of evaluating the merits and risks of its
     investment and has the ability to suffer the total loss of the investment.
     The Warrant Holder further represents that it has had the opportunity to
     ask questions of and receive answers from the Company concerning the terms
     and conditions of the Warrants, the business of the Company, and to obtain
     additional information to such Warrant Holder's satisfaction. The Warrant
     Holder also understands that shares of Common Stock issued upon exercise of
     Warrants shall be stamped or imprinted with a legend in substantially the
     following form:

      "THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
      1933, AS AMENDED, OR ANY STATE SECURITIES LAW. THEY MAY NOT BE SOLD OR
      OFFERED FOR SALE, PLEDGED, HYPOTHECATED OR OTHERWISE TRANSFERRED IN THE
      ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT RELATED THERETO UNDER SAID
      ACT AND APPLICABLE STATE SECURITIES LAWS OR UNLESS THE COMPANY HAS
      RECEIVED AN OPINION OF COUNSEL THAT SUCH REGISTRATION IS NOT REQUIRED TO
      EFFECTUATE SUCH TRANSACTION."

          (c)  Accredited Investor.  The Warrant Holder is an "Accredited
               -------------------
     Investor" within the meaning of Rule 501 of Regulation D under the
     Securities Act, as presently in effect.

     5.   Other Notices. If any time prior to the earlier to occur of (i) the
          -------------
Expiration of the Warrants evidenced hereby and (ii) the Company's initial
public offering of its Common Stock:

          (a)  The Company shall declare any dividend on the Common Shares
     payable in shares of capital stock of the Company other than Common Shares;
     or

          (b)  The Company shall issue any options, warrants or rights pro rata
     to all holders of Common Shares entitling them to subscribe for or purchase
     any shares of stock of the Company or to receive any other rights; or

          (c)  The Company shall distribute pro rata to all holders of Common
     Shares of evidences of its indebtedness or assets (excluding cash
     distributions paid out of retained earnings or retained surplus); or

          (d)  There shall occur any reclassification of the Common Shares, or
     any consolidation or merger of the Company with or into another corporation
     (other than a consolidation or merger in which the Company is the
     continuing corporation and which does not result in any reclassification of
     the Common Stock) or a sale or transfer to another corporation of all or
     substantially all of the properties of the Company; or

                                       4
<PAGE>

          (e)  There shall occur the voluntary or involuntary liquidation,
     dissolution or winding up of the affairs of the Company;

then, and in each of such cases, the Company shall use commercially reasonable
efforts to mail to the registered holder hereof at its last address appearing on
the books of the Company, a reasonable time prior to the applicable record date
(or determination date) mentioned below, a notice stating, to the extent such
information is available, (i) the date on which a record is to be taken for the
purpose of such dividend, distribution or rights, or, if a record is not to be
taken, the date as of which the holders of Common Shares or of record to be
entitled to such dividend, distribution or rights are to be determined, or (ii)
the date on which such liquidation, dissolution or winding up is expected to
become effective and the date as of which it is expected that holders of Common
Shares of record shall be entitled to exchange their Common Shares for
securities or other property deliverable upon such reclassification,
consolidation, merger, sale, transfer, liquidation, dissolution or winding up.

     6.   Replacement of Warrants.  On receipt of evidence reasonably
          -----------------------
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant Certificate, and in the case of any such loss, theft or destruction
of this Warrant Certificate, on delivery of an indemnity agreement or security
reasonably satisfactory in form and amount to the Company or, in the case of any
such mutilation, on surrender and cancellation of such Warrant Certificate,
unless the Company has received notice that any such Warrant Certificate has
been acquired by a bona fide purchase, the Company at its expense will execute
and deliver, in lieu thereof, a new Warrant Certificate of like tenor.

     7.   Registered Holder.  The registered holder of this Warrant Certificate
          -----------------
shall be deemed the owner hereof and of the Warrants evidenced hereby for all
purposes.  The registered holder of this Warrant Certificate shall not be
entitled by virtue of ownership of this Warrant Certificate to any rights
whatsoever as a shareholder of the Company.

     8.   Amendments and Waivers. Any provision in this Warrant Certificate to
          ----------------------
the contrary notwithstanding, changes in or additions to this Warrant
Certificate may be made and compliance with any covenant or provision herein set
forth may be omitted or waived if the Company shall obtain consent thereto in
writing from persons holding at least a majority of the aggregate of the then
outstanding Warrants. The Company shall, in each such case, deliver copies of
such consent in writing to any holders who did not execute the same.

     9.   Transfer.
          --------

          (a)  None of (a) this Warrant Certificate, (b) the Warrants evidenced
     hereby or (c) any Common Shares issued upon exercise hereof may be sold,
     transferred, pledged, hypothecated or otherwise disposed of unless and
     until:  (i) (x) there is then in effect a registration statement under the
     Securities Act of 1933, as amended (the "Securities Act"), covering such
     proposed disposition and

                                       5
<PAGE>

     such disposition is made in accordance with such registration statement and
     all applicable state securities laws; or (y) (A) the transferor shall have
     notified the Company of the proposed disposition and shall have furnished
     the Company with a statement of the circumstances surrounding the proposed
     disposition, and (B) if reasonably requested by the Company, such
     transferor shall have furnished the Company with an opinion of counsel,
     reasonably satisfactory to the Company, that such disposition will not
     require registration of such securities under the Securities Act and that
     all requisite action has been or will, on a timely basis, be taken under
     any applicable state securities laws in connection with such disposition;
     and (ii) the proposed transferee shall have agreed in writing to be bound
     by the terms and provisions of this Section 9.

          (b)  Notwithstanding the provisions of paragraphs (i) above, no such
     registration statement or opinion of counsel shall be necessary for a
     transfer pursuant to Rule 144(k) promulgated under the Securities Act, or a
     transfer to an entity wholly owned by such transferor, if the transferee
     agrees in writing to be subject to the terms hereof to the same extent as
     if such transferee were an original holder of this certificate.

     10.  Miscellaneous.
          -------------

          (a)  Registration Rights.  With respect to Common Shares issued upon
     exercise of this Warrant Certificate, Warrant Holder will be entitled to
     Incidental Registration Rights pursuant to Section 3 of that certain
     Registration Rights Agreement, dated as of August 8, 2000 (the
     "Registration Rights Agreement"), by and among the Company and the Holders
      -----------------------------
     (as defined therein), as if (a) Warrant Holder was a Stockholder (as
     defined in the Registration Rights Agreement) and (b) the Common Shares
     acquired upon exercise of Warrants were Registrable Securities (as defined
     in the Registration Rights Agreement and as used herein). In addition,
     Warrant Holder agrees to (i) be subject to all of the Limitations, (ii)
     abide by all of the procedures and (iii) be governed by all other
     provisions of the Registration Rights Agreement otherwise applicable to a
     Stockholder participating in an Incidental Registration pursuant to Section
     3 of the Registration Rights Agreement. Any Common Shares deemed
     Registrable Securities pursuant to this Section shall cease to be deemed
     Registrable Securities when Registrable Securities cease to be Registrable
     Securities under the Registration Rights Agreement.

          (b)  Notices. All notices, requests, consents, demands and other
               -------
     communications hereunder shall be in writing and mailed, faxed or delivered
     to each party as follows:

if to the Company: Control Delivery Systems, Inc., 313 Pleasant St., Watertown,
MA 02472, facsimile: 617.926.2313, Attention: Paul Ashton, with a copy to: Ropes
& Gray, One International Place, Boston, MA 02110, facsimile: (617) 951-7050,
Attention: Mary E. Weber, Esq.; and if to the Warrant Holder: Deutsche Bank
Securities Inc., facsimile: (410) 895-4582, Attention: Thomas J. DeRosa.

All such notices, requests, demands and other communications shall be effective,
(a) when mailed (which mailing must be accomplished by certified or registered
mail, return receipt

                                       6
<PAGE>

requested, postage prepaid), five days after deposited in the mails, (b) when
sent by express overnight courier service one day after properly deposited with
such courier service, or (c) when faxed upon confirmed transmission by
facsimile.

          (c)  Successors and Assigns; Third Party Beneficiaries. This Warrant
     Certificate shall inure to the benefit of and be binding upon the
     successors and permitted assigns of the parties hereto.

          (d)  Counterparts. This Warrant Certificate may be executed in any
               ------------
     number of counterparts and by the parties hereto in separate counterparts,
     each of which when so executed shall be deemed to be an original and all of
     which taken together shall constitute one and the same agreement.

          (e)  Governing Law.  THIS WARRANT CERTIFICATE SHALL BE GOVERNED BY AND
               -------------
     CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE, WITHOUT
     REGARD TO THE PRINCIPLES OF CONFLICTS OF LAW OF ANY JURISDICTION.  Any
     judicial proceeding brought with respect to this Warrant Certificate must
     be brought in any court of competent jurisdiction in The Commonwealth of
     Massachusetts, and, by execution and delivery of this Warrant Certificate,
     the Company and the Warrant Holder each (i) accept generally and
     unconditionally, the exclusive jurisdiction of such courts, and irrevocably
     agree to be bound by any judgment rendered thereby in connection with this
     Warrant Certificate and (ii) irrevocably waive any objection it may now or
     hereafter have as to the venue of any such suit, action or proceeding
     brought in such a court or that such court is an inconvenient forum.

          (f)  Severability. If any one or more of the provisions contained
               ------------
     herein, or the application thereof in any circumstance, is held invalid,
     illegal or unenforceable in any respect for any reason, the validity,
     legality and enforceability of any such provision in every other respect
     and of the remaining provisions hereof shall not be in any way impaired,
     unless the provisions held invalid, illegal or unenforceable shall
     substantially impair the benefits of the remaining provisions hereof.

          (g)  Entire Agreement.
               ----------------

               (i)  This Warrant Certificate, together with the exhibits and
          schedules hereto is intended by the parties as a final expression of
          their agreement and intended to be a complete and exclusive statement
          of the agreement and understanding of the parties hereto in respect of
          the subject matter contained herein and therein. There are no
          restrictions, promises, warranties or undertakings, other than those
          set forth or referred to herein or therein. This Warrant Certificate,
          together with the exhibits and schedules, supersedes all prior
          agreements and understandings between the parties with respect to such
          subject matter.

               (ii) The parties hereto agree and acknowledge that this Warrant
          Certificate and the Warrants issued hereunder are the warrants
          referred to in

                                       7
<PAGE>

       Section 4 of the letter agreement, dated as of April 7, 2000 (the
       "Engagement Letter"), between the Company and Deutsche Bank Securities
        -----------------
       Inc. The parties further agree that following execution and delivery of
       this Warrant Certificate, the Company shall have no further obligations
       to Deutsche Bank Securities Inc. pursuant to Section 4 of the Engagement
       Letter.

       (h)  Further Assurances. Each of the parties shall execute such
            ------------------
documents and perform such further acts (including, without limitation,
obtaining any consents, exemptions, authorizations or other actions by, or
giving any notices to, or making any filings with, any Governmental Authority or
any other Person, and otherwise fulfilling, or causing the fulfillment of, the
various obligations made herein), as may be reasonably required or desirable to
carry out or to perform the provisions of this Warrant Certificate and to
consummate and make effective as promptly as possible the transactions
contemplated by this Warrant Certificate.

                 [Remainder of Page Intentionally left Blank]

                                       8
<PAGE>

     IN WITNESS WHEREOF, CONTROL DELIVERY SYSTEMS, INC. has caused this Warrant
Certificate to be signed by a duly authorized officer under seal, and the
undersigned Warrant Holder hereby agrees and accepts the terms of this Warrant
Certificate to be dated January 12, 2001.


COMPANY:                      CONTROL DELIVERY SYSTEMS, INC.

                              By: /s/ Paul Ashton
                                  -------------------------------
                                  Name:   Paul Ashton
                                  Title:  President and CEO


ACCEPTED AND AGREED:

WARRANT HOLDER:               DEUTSCHE BANK SECURITIES INC.


DATE: January 12, 2001        By: /s/ Thomas J. DeRosa
      ----------------            -------------------------------
                                  Name:   Thomas J. DeRosa
                                  Title:  Managing Director

                                       9
<PAGE>

                                                                       EXHIBIT A
                                                                       ---------


                              NOTICE OF EXERCISE


    To:  Control Delivery Systems, Inc.

    1.   The undersigned hereby elects to purchase __________ shares of the
         Common Stock of Control Delivery Systems, Inc. pursuant to the terms of
         the Warrant Certificate, dated as of August 8, 2000, by and between
         Control Delivery Systems, Inc. and the undersigned and tenders herewith
         payment of the purchase price of such shares in full.

    2.   Please issue a certificate or certificates representing said shares in
         the name of the undersigned.



                                                   DEUTSCHE BANK SECURITIES INC.



                                                   By:  _______________________
                                                        Name:
                                                        Title:



Date:  _____________________

                                       10