<PAGE>

                                                                    Exhibit 10.7

THIS WARRANT AND THE WARRANT SHARES SHALL NOT BE SOLD OR TRANSFERRED EXCEPT (A)
 IN ACCORDANCE WITH THE PROVISIONS OF REGULATION S UNDER THE SECURITIES ACT OF
   1933, (B) PURSUANT TO REGISTRATION UNDER THE SECURITIES ACT OF 1933 OR (C)
PURSUANT TO AN AVAILABLE EXEMPTION FROM REGISTRATION UNDER THE SECURITIES ACT OF
1933. HEDGING TRANSACTIONS INVOLVING THIS WARRANT AND THE WARRANT SHARES MAY NOT
       BE CONDUCTED UNLESS IN COMPLIANCE WITH THE SECURITIES ACT OF 1933.

THIS WARRANT AND THE SHARES OF COMMON STOCK ISSUED UPON ITS EXERCISE ARE SUBJECT
     TO THE RESTRICTIONS ON TRANSFER SET FORTH IN SECTION 5 OF THIS WARRANT

Warrant No. 2006-1                                   Number of Shares: 6,093,750
                                                         (subject to adjustment)
Date of Issuance: March 24, 2006

                           IDERA PHARMACEUTICALS, INC.

                          Common Stock Purchase Warrant

                         (Void after September 24, 2011)

     Idera Pharmaceuticals, Inc., a Delaware corporation (the "Company"), for
value received, hereby certifies that Biotech Shares Ltd., or its registered
assigns (the "Registered Holder"), is entitled, subject to the terms and
conditions set forth below, to purchase from the Company, at any time, or from
time to time, on or after September 24, 2006 and on or before 5:00 p.m. (Boston
time) on September 24, 2011, 6,093,750 shares of Common Stock, $0.001 par value
per share, of the Company ("Common Stock"), at a purchase price of $0.74 per
share. The shares purchasable upon exercise of this Warrant, and the purchase
price per share, each as adjusted from time to time pursuant to the provisions
of this Warrant, are hereinafter referred to as the "Warrant Shares" and the
"Purchase Price," respectively.

     1. Exercise.

          (a) Exercise Process. The Registered Holder may, at its option, elect
to exercise this Warrant, in whole or in part and at any time, or from time to
time, by surrendering this Warrant, with the purchase form appended hereto as
Exhibit I duly executed by or on behalf of the Registered Holder, at the
principal office of the Company, or at such other office or agency as the
Company may designate, accompanied by payment in full, in lawful money of the
United States, of the Purchase Price payable in respect of the number of Warrant
Shares purchased upon such exercise.

          (b) Exercise Date. Each exercise of this Warrant shall be deemed to
have been effected immediately prior to the close of business on the day on
which this Warrant shall have been surrendered to the Company as provided in
subsection 1(a) above (the "Exercise Date"). At such time, the person or persons
in whose name or names any certificates for Warrant Shares shall be issuable
upon such exercise as provided in subsection 1(c) below shall be deemed

<PAGE>

to have become the holder or holders of record of the Warrant Shares represented
by such certificates.

          (c) Issuance of Common Stock Certificates. As soon as practicable
after the exercise of this Warrant in whole or in part, and in any event within
10 days thereafter, the Company, at its expense, will cause to be issued in the
name of, and delivered to, the Registered Holder, or as the Registered Holder
(upon payment by the Registered Holder of any applicable transfer or withholding
taxes) may direct:

               (i) a certificate or certificates for the number of full Warrant
Shares to which the Registered Holder shall be entitled upon such exercise plus,
in lieu of any fractional share to which the Registered Holder would otherwise
be entitled, cash in an amount determined pursuant to Section 3 hereof; and

               (ii) in case such exercise is in part only, a new warrant or
warrants (dated the date hereof) of like tenor, calling in the aggregate on the
face or faces thereof for the number of Warrant Shares equal (without giving
effect to any adjustment therein) to the number of such shares called for on the
face of this Warrant minus the number of Warrant Shares for which this Warrant
was so exercised.

          (d) Exercise by Non-U.S. Person. It shall be a condition to the
exercise of this Warrant by a Registered Holder that is not a U.S. Person (as
defined under the Securities Act of 1933, as amended (the "Securities Act"))
that such Registered Holder certify in writing to the Company that it is not a
U.S. Person and that this Warrant is not being exercised on behalf of a U.S.
Person.

     2. Adjustments.

          (a) Adjustment for Stock Splits and Combinations. If the Company shall
at any time, or from time to time after the date on which this Warrant was first
issued (or, if this Warrant was issued upon partial exercise of, or in
replacement of, another warrant of like tenor, then the date on which such
original warrant was first issued) (either such date being referred to as the
"Original Issue Date") effect a subdivision of the outstanding Common Stock, the
Purchase Price then in effect immediately before that subdivision shall be
proportionately decreased. If the Company shall at any time, or from time to
time, after the Original Issue Date combine the outstanding shares of Common
Stock, the Purchase Price then in effect immediately before the combination
shall be proportionately increased. Any adjustment under this paragraph shall
become effective at the close of business on the date the subdivision or
combination becomes effective.

          (b) Adjustment for Certain Dividends and Distributions. In the event
the Company at any time, or from time to time after the Original Issue Date
shall make or issue, or fix a record date for the determination of holders of
Common Stock entitled to receive, a dividend or other distribution payable in
additional shares of Common Stock, then and in each such event the Purchase
Price then in effect immediately before such event shall be decreased as of the
time of such issuance or, in the event such a record date shall have been fixed,
as of the


                                      -2-

<PAGE>

close of business on such record date, by multiplying the Purchase Price then
in effect by a fraction:

               (i) the numerator of which shall be the total number of shares of
Common Stock issued and outstanding immediately prior to the time of such
issuance or the close of business on such record date, and

               (ii) the denominator of which shall be the total number of shares
of Common Stock issued and outstanding immediately prior to the time of such
issuance or the close of business on such record date plus the number of shares
of Common Stock issuable in payment of such dividend or distribution;

provided, however, that if such record date shall have been fixed and such
dividend is not fully paid or if such distribution is not fully made on the date
fixed therefor, the Purchase Price shall be recomputed accordingly as of the
close of business on such record date and thereafter the Purchase Price shall be
adjusted pursuant to this paragraph as of the time of actual payment of such
dividends or distributions.

          (c) Adjustment in Number of Warrant Shares. When any adjustment is
required to be made in the Purchase Price pursuant to subsections 2(a) or 2(b)
above, the number of Warrant Shares purchasable upon the exercise of this
Warrant shall be changed to the number determined by dividing (i) an amount
equal to the number of shares issuable upon the exercise of this Warrant
immediately prior to such adjustment, multiplied by the Purchase Price in effect
immediately prior to such adjustment, by (ii) the Purchase Price in effect
immediately after such adjustment.

          (d) Adjustments for Other Dividends and Distributions. In the event
the Company at any time, or from time to time after the Original Issue Date
shall make or issue, or fix a record date for the determination of holders of
Common Stock entitled to receive, a dividend or other distribution payable in
securities of the Company (other than shares of Common Stock) or in cash or
other property (other than regular cash dividends paid out of earnings or earned
surplus, determined in accordance with generally accepted accounting
principles), then and in each such event provision shall be made so that the
Registered Holder shall receive upon exercise hereof, in addition to the number
of shares of Common Stock issuable hereunder, the kind and amount of securities
of the Company, cash or other property which the Registered Holder would have
been entitled to receive had this Warrant been exercised on the date of such
event and had the Registered Holder thereafter, during the period from the date
of such event to and including the Exercise Date, retained any such securities
receivable during such period, giving application to all adjustments called for
during such period under this Section 2 with respect to the rights of the
Registered Holder.

          (e) Adjustment for Reorganization. If there shall occur any
reorganization, recapitalization, reclassification, consolidation or merger
involving the Company in which the Common Stock is converted into or exchanged
for securities, cash or other property (other than a transaction covered by
subsections 2(a), 2(b) or 2(d)) (collectively, a "Reorganization"), then,
following such Reorganization, the Registered Holder shall receive upon exercise
hereof the kind and amount of securities, cash or other property which the
Registered Holder would have been


                                      -3-

<PAGE>

entitled to receive pursuant to such Reorganization if such exercise had taken
place immediately prior to such Reorganization. In any such case, appropriate
adjustment (as determined in good faith by the Board of Directors of the Company
(the "Board")) shall be made in the application of the provisions set forth
herein with respect to the rights and interests thereafter of the Registered
Holder, to the end that the provisions set forth in this Section 2 (including
provisions with respect to changes in and other adjustments of the Purchase
Price) shall thereafter be applicable, as nearly as reasonably may be, in
relation to any securities, cash or other property thereafter deliverable upon
the exercise of this Warrant.

          (f) Certificate as to Adjustments. Upon the occurrence of each
adjustment or readjustment of the Purchase Price pursuant to this Section 2, the
Company at its expense shall, as promptly as reasonably practicable but in any
event not later than 30 days thereafter, compute such adjustment or readjustment
in accordance with the terms hereof and furnish to the Registered Holder a
certificate setting forth such adjustment or readjustment (including the kind
and amount of securities, cash or other property for which this Warrant shall be
exercisable and the Purchase Price) and showing in detail the facts upon which
such adjustment or readjustment is based. The Company shall, as promptly as
reasonably practicable after the written request at any time of the Registered
Holder (but in any event not later than 30 days thereafter), furnish or cause to
be furnished to the Registered Holder a certificate setting forth (i) the
Purchase Price then in effect and (ii) the number of shares of Common Stock and
the amount, if any, of other securities, cash or property which then would be
received upon the exercise of this Warrant.

     3. Fractional Shares. The Company shall not be required upon the exercise
of this Warrant to issue any fractional shares, but shall pay the value thereof
to the Registered Holder in cash on the basis of the Fair Market Value per share
of Common Stock. The "Fair Market Value" per share of Common Stock shall be
determined as follows:

          (a) If the Common Stock is listed on a national securities exchange,
the Nasdaq National Market, the Nasdaq Capital Market, the OTC Bulletin Board or
another nationally recognized trading system as of the Exercise Date, the Fair
Market Value per share of Common Stock shall be deemed to be the average of the
high and low reported sale prices per share of Common Stock thereon for the five
consecutive trading day period immediately preceding the Exercise Date; provided
that if the Common Stock is not so listed during such period, the Fair Market
Value per share of Common Stock shall be determined pursuant to clause 3(b).

          (b) If the Common Stock is not listed on a national securities
exchange, the Nasdaq National Market, the Nasdaq Capital Market, the OTC
Bulletin Board or another nationally recognized trading system as of the
Exercise Date, the Fair Market Value per share of Common Stock shall be deemed
to be the amount most recently determined by the Board or an authorized
committee of the Board to represent the fair market value per share of the
Common Stock (including without limitation a determination for purposes of
granting Common Stock options or issuing Common Stock under any plan, agreement
or arrangement with employees of the Company).

     4. Redemption of Warrants.


                                      -4-

<PAGE>

          (a) Subject to the terms of this Section 4, the Company shall have the
right to redeem this Warrant for a redemption price (the "Redemption Price")
equal to the result obtained by multiplying (i) $0.01 by (ii) the number of
Warrant Shares that the Registered Holder is entitled to purchase upon exercise
of this Warrant immediately prior to the termination of this Warrant under
Section 4(d) below (such Redemption Price being subject to adjustment for stock
splits, stock dividends, combinations, recapitalizations, reclassifications, and
similar transactions affecting the Common Stock).

          (b) The Company shall exercise this redemption right by providing at
least 30 days' prior written notice to the Registered Holder of such redemption
(the "Redemption Notice"). Such Redemption Notice shall be provided to the
Registered Holder in accordance with Section 10 of this Warrant. The Redemption
Notice shall specify the time, manner and place of redemption, including without
limitation the date on which this Warrant shall be redeemed (the "Redemption
Date") and the Redemption Price payable to the Registered Holder (assuming that
this Warrant is not exercised on or prior to the Redemption Date).

          (c) Notwithstanding the foregoing, the Company may not redeem this
Warrant or provide the Redemption Notice to the Registered Holder (i) prior to
March 24, 2010 and (ii) unless the closing sales price of the Common Stock on
each day of a 15 consecutive trading day period ending within 30 days prior to
the date the Company provides the Redemption Notice to the Registered Holder is
greater than or equal to 250% of the Purchase Price then in effect.

          (d) This Warrant shall cease to be exercisable and shall be terminated
and of no further force or effect effective at 5:00 p.m. (Boston Time) on the
Redemption Date. If the Registered Holder does not exercise this Warrant on or
prior to the Redemption Date, the Registered Holder shall surrender this Warrant
to the Company on the Redemption Date for cancellation. From and after the
Redemption Date, the Registered Holder's sole right hereunder shall be to
receive the Redemption Price, without interest, upon presentation and surrender
of this Warrant for cancellation.

     5. Transfers, etc.

          (a) Neither this Warrant nor the Warrant Shares shall be sold or
transferred unless either (i) they first shall have been registered under the
Securities Act, or (ii) the Company first shall have been furnished with an
opinion of legal counsel, reasonably satisfactory to the Company, to the effect
that such sale or transfer is exempt from the registration requirements of the
Securities Act. Notwithstanding the foregoing, no registration or opinion of
counsel shall be required for a transfer made in accordance with Rule 144 under
the Securities Act.

          (b) Each certificate representing Warrant Shares shall bear a legend
substantially in the following form:

               "The securities represented by this certificate have not been
               registered under the Securities Act of 1933, as amended, and may
               not be offered, sold or otherwise transferred, pledged or
               hypothecated unless and until such securities are registered
               under such Act or an opinion of counsel


                                      -5-

<PAGE>

               satisfactory to the Company is obtained to the effect that such
               registration is not required."

The foregoing legend shall be removed from the certificates representing any
Warrant Shares, at the request of the holder thereof, at such time as they
become eligible for resale pursuant to Rule 144(k) under the Securities Act.

          (c) In the case of a Registered Holder that is a non-U.S. Person:

               (i) THIS WARRANT AND THE WARRANT SHARES HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933 AND THIS WARRANT MAY NOT BE EXERCISED BY OR ON
BEHALF OF A U.S. PERSON UNLESS REGISTERED UNDER THE SECURITIES ACT OF 1933 OR AN
EXEMPTION FROM SUCH REGISTRATION IS AVAILABLE.

               (ii) This Warrant and the Warrant Shares shall not be sold or
transferred except (A) in accordance with the provisions of Regulation S under
the Securities Act, (B) pursuant to registration under the Securities Act or (C)
pursuant to an available exemption from registration under the Securities Act.
Hedging transactions involving this Warrant and the Warrant Shares may not be
conducted unless in compliance with the Securities Act.

               (iii) Notwithstanding Section 5(b) to the contrary, each
certificate representing Warrant Shares issued to a Registered Holder that is a
non-U.S. Person shall bear a legend substantially in the following form:

     "These shares have not been registered under the Securities Act of 1933.
     They may not be offered or transferred by sale, assignment, pledge or
     otherwise unless (i) a registration statement for the shares under the
     Securities Act of 1933 is in effect or (ii) the corporation has received an
     opinion of counsel, which opinion is satisfactory to the corporation, to
     the effect that such registration is not required under the Securities Act
     of 1933 or (iii) such offer or transfer is made in accordance with the
     provisions of Regulation S under the Securities Act of 1933. Hedging
     transactions involving these shares may not be conducted unless in
     compliance with the Securities Act of 1933."

          (d) The Company has agreed pursuant to the Registration Rights
Agreement dated as of March 24, 2006 by and among the Company, Biotech Shares
Ltd. and the Agent (as defined therein) to file a registration statement with
the U.S. Securities and Exchange Commission to register the Warrant Shares under
the Securities Act. The Company shall remove the legend on any certificate
representing Warrant Shares if such Warrant Shares are resold or transferred
pursuant to an effective registration statement under the Securities Act.

          (e) The Company will maintain a register containing the name and
address of the Registered Holder of this Warrant. The Registered Holder may
change its address as shown on the warrant register by written notice to the
Company requesting such change.


                                      -6-

<PAGE>

          (f) Notwithstanding Section 5(a) above, a Registered Holder which is
an entity may transfer this Warrant, in whole, to a wholly owned subsidiary or a
shareholder of such entity, a Registered Holder which is a partnership may
transfer this Warrant, in whole, to a partner of such partnership or a retired
partner of such partnership or to the estate of any such partner or retired
partner, a Registered Holder which is a limited liability company may transfer
this Warrant, in whole, to a member of such limited liability company or a
retired member or to the estate of any such member or retired member and a
Registered Holder who is an individual may transfer this Warrant, in whole, to
such individual's spouse, children, parents, siblings, grandchildren or any
trust established exclusively for the benefit of one or more of the foregoing
individuals, or by will or the laws of descent and distribution (in each case, a
"Permitted Transferee"). This Warrant and all rights hereunder are transferable
to a Permitted Transferee, in whole, upon surrender of this Warrant with a
properly executed assignment (in the form of Exhibit II hereto) at the principal
office of the Company (or, if another office or agency has been designated by
the Company for such purpose, then at such other office or agency).

     6. No Impairment. The Company will not, by amendment of its charter or
through any reorganization, transfer of assets, consolidation, merger,
dissolution, issue or sale of securities or any other voluntary action, avoid or
seek to avoid the observance or performance of any of the terms of this Warrant,
but will at all times in good faith assist in the carrying out of all such terms
and in the taking of all such action as may be necessary or appropriate in order
to protect the rights of the Registered Holder against impairment.

     7. Notices of Record Date, etc. In the event:

          (a) the Company shall take a record of the holders of its Common Stock
(or other stock or securities at the time deliverable upon the exercise of this
Warrant) for the purpose of entitling or enabling them to receive any dividend
or other distribution, or to receive any right to subscribe for or purchase any
shares of stock of any class or any other securities, or to receive any other
right; or

          (b) of any capital reorganization of the Company, any reclassification
of the Common Stock of the Company, any consolidation or merger of the Company
with or into another corporation (other than a consolidation or merger in which
the Company is the surviving entity and its Common Stock is not converted into
or exchanged for any other securities or property), or any transfer of all or
substantially all of the assets of the Company; or

          (c) of the voluntary or involuntary dissolution, liquidation or
winding-up of the Company,

then, and in each such case, the Company will send or cause to be sent to the
Registered Holder a notice specifying, as the case may be, (i) the record date
for such dividend, distribution or right, and the amount and character of such
dividend, distribution or right, or (ii) the effective date on which such
reorganization, reclassification, consolidation, merger, transfer, dissolution,
liquidation or winding-up is to take place, and the time, if any is to be fixed,
as of which the holders of record of Common Stock (or such other stock or
securities at the time deliverable upon the exercise of this Warrant) shall be
entitled to exchange their shares of Common Stock (or such other stock or
securities) for securities or other property deliverable upon such


                                      -7-

<PAGE>

reorganization, reclassification, consolidation, merger, transfer, dissolution,
liquidation or winding-up. Such notice shall be sent at least 10 days prior to
the record date or effective date for the event specified in such notice.

     8. Reservation of Stock. The Company will at all times reserve and keep
available, solely for issuance and delivery upon the exercise of this Warrant,
such number of Warrant Shares and other securities, cash and/or property, as
from time to time shall be issuable upon the exercise of this Warrant.

     9. Exchange or Replacement of Warrants.

          (a) Upon the surrender by the Registered Holder, properly endorsed, to
the Company at the principal office of the Company, the Company will, subject to
the provisions of Section 5 hereof, issue and deliver to or upon the order of
the Registered Holder, at the Company's expense, a new Warrant or Warrants of
like tenor, in the name of the Registered Holder or as the Registered Holder
(upon payment by the Registered Holder of any applicable transfer taxes) may
direct, calling in the aggregate on the face or faces thereof for the number of
shares of Common Stock (or other securities, cash and/or property) then issuable
upon exercise of this Warrant.

          (b) Upon receipt of evidence reasonably satisfactory to the Company of
the loss, theft, destruction or mutilation of this Warrant and (in the case of
loss, theft or destruction) upon delivery of an indemnity agreement (with surety
if reasonably required) in an amount reasonably satisfactory to the Company, or
(in the case of mutilation) upon surrender and cancellation of this Warrant, the
Company will issue, in lieu thereof, a new Warrant of like tenor.

     10. Notices. All notices and other communications from the Company to the
Registered Holder in connection herewith shall be mailed by certified or
registered mail, postage prepaid, or sent via a reputable overnight courier
service to the address last furnished to the Company in writing by the
Registered Holder. All notices and other communications from the Registered
Holder to the Company in connection herewith shall be mailed by certified or
registered mail, postage prepaid, or sent via a reputable overnight courier
service to the Company at its principal office set forth below. If the Company
should at any time change the location of its principal office to a place other
than as set forth below, it shall give prompt written notice to the Registered
Holder and thereafter all references in this Warrant to the location of its
principal office at the particular time shall be as so specified in such notice.
All such notices and communications shall be deemed delivered (i) two business
days after being sent by certified or registered mail, return receipt requested,
postage prepaid, or (ii) two business days after being sent via a reputable
overnight courier service.

     11. No Rights as Stockholder. Until the exercise of this Warrant, the
Registered Holder shall not have or exercise any rights by virtue hereof as a
stockholder of the Company. Notwithstanding the foregoing, in the event (i) the
Company effects a split of the Common Stock by means of a stock dividend and the
Purchase Price of and the number of Warrant Shares are adjusted as of the date
of the distribution of the dividend (rather than as of the record date for such
dividend), and (ii) the Registered Holder exercises this Warrant between the
record date and the distribution date for such stock dividend, the Registered
Holder shall be entitled to receive,


                                      -8-

<PAGE>

on the distribution date, the stock dividend with respect to the shares of
Common Stock acquired upon such exercise, notwithstanding the fact that such
shares were not outstanding as of the close of business on the record date for
such stock dividend.

     12. Amendment or Waiver. Any term of this Warrant may be amended or waived
only by an instrument in writing signed by the party against which enforcement
of the change or waiver is sought. No waivers of any term, condition or
provision of this Warrant, in any one or more instances, shall be deemed to be,
or construed as, a further or continuing waiver of any such term, condition or
provision.

     13. Section Headings. The section headings in this Warrant are for the
convenience of the parties and in no way alter, modify, amend, limit or restrict
the contractual obligations of the parties.

     14. Governing Law. This Warrant will be governed by and construed in
accordance with the internal laws of the State of Delaware (without reference to
the conflicts of law provisions thereof).

     15. Facsimile Signatures. This Warrant may be executed by facsimile
signature.

     16. Acceptance by Registered Holder. By acquiring and accepting this
Warrant, the Registered Holder shall be deemed to have agreed and accepted the
terms and conditions of this Warrant.

     EXECUTED as of the Date of Issuance indicated above.

                                        IDERA PHARMACEUTICALS, INC.


                                        By: /s/ Sudhir Agrawal
                                            ------------------------------------
                                        Title: Chief Executive Officer


                                      -9-

<PAGE>

                                                                       EXHIBIT I

                                  PURCHASE FORM

To: Idera Pharmaceuticals, Inc.                               Dated: ___________

     The undersigned, pursuant to the provisions set forth in the attached
Warrant (No. ______), hereby elects to purchase __________ shares of the Common
Stock of Idera Pharmaceuticals, Inc. covered by such Warrant.

     The undersigned herewith makes a payment of $___________ representing the
full purchase price for such shares at the price per share provided for in such
Warrant.


                                        Signature:
                                                   -----------------------------
                                        Address:
                                                 -------------------------------

                                                 -------------------------------


                                      -10-

<PAGE>

                                                                      EXHIBIT II

                                 ASSIGNMENT FORM

     FOR VALUE RECEIVED, ________________________________________ hereby sells,
assigns and transfers all of the rights of the undersigned under the attached
Warrant (No. ____) with respect to all of the shares of Common Stock of Idera
Pharmaceuticals, Inc. covered thereby set forth below, unto:

<TABLE>
<S>                <C>       <C>
Name of Assignee   Address   No. of Shares

</TABLE>


Dated: ____________________             Signature:
                                                   -----------------------------


Signature Guaranteed:


By:
    ------------------------------------

The signature should be guaranteed by an eligible guarantor institution (banks,
stockbrokers, savings and loan associations and credit unions with membership in
an approved signature guarantee medallion program) pursuant to Rule 17Ad-15
under the Securities Exchange Act of 1934.


                                      -11-