POWER OF ATTORNEY

       Know all by these presents, that the undersigned hereby constitutes and
appoints each of (i) the Chief Executive Officer of BIND Therapeutics, Inc.
(the "Company"), who is currently Scott Minick, (ii) the Company's Chief
Financial Officer, who is currently Andrew Hirsch and (iii) the Company's
Controller, who is currently Kristin Rydzewski, and their respective successors,
signing singly, the undersigned's true and lawful attorney-in-fact to:

       (1) prepare, execute in the undersigned's name and on the undersigned's
       behalf, and submit to the U.S. Securities and Exchange Commission (the
       "SEC") a Form ID, including amendments thereto, and any other documents
       necessary or appropriate to obtain codes and passwords enabling the
       undersigned to make electronic filings with the SEC of reports required
       by Section 16(a) of the Securities Exchange Act of 1934 or any rule or
       regulation of the SEC;

       (2) execute for and on behalf of the undersigned, in the undersigned's
       capacity as an officer and/or director of the Company, and/or 10% holder
       of the Company's capital stock, Forms 3, 4, and 5 and any amendments
       thereto in accordance with Section 16(a) of the Securities Exchange Act
       of 1934 and the rules thereunder;

       (3) do and perform any and all acts for and on behalf of the undersigned
       which may be necessary or desirable to complete and execute any such Form
       3, 4, or 5, complete and execute any amendment or amendments thereto, and
       timely file such form with the SEC and any stock exchange or similar
       authority; and

       (4) take any other action of any type whatsoever in connection with the
       foregoing which, in the opinion of such attorney-in-fact, may be of
       benefit to, in the best interest of, or legally required by, the
       undersigned, it being understood that the documents executed by such
       attorney-in-fact on behalf of the undersigned pursuant to this Power of
       Attorney shall be in such form and shall contain such terms and
       conditions as such attorney-in-fact may approve in such
       attorney-in-fact's discretion.

       The undersigned hereby grants to each such attorney-in-fact full
power and authority to do and perform any and every act and thing whatsoever
requisite, necessary, or proper to be done in the exercise of any of the rights
and powers herein granted, as fully to all intents and purposes as the
undersigned might or could do if personally present, with full power of
substitution or revocation, hereby ratifying and confirming all that such
attorney-in-fact, or such attorney-in-fact's substitute or substitutes, shall
lawfully do or cause to be done by virtue of this power of attorney and the
rights and powers herein granted. The undersigned acknowledges that the
foregoing attorneys-in-fact, in serving in such capacity at the request of the
undersigned, are not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 of the Securities
Exchange Act of 1934.

       The undersigned agrees that each such attorney-in-fact herein may rely
entirely on information furnished orally or in writing by the undersigned to
such attorney-in-fact. The undersigned also agrees to indemnify and hold
harmless the Company and each such attorney-in-fact against any losses, claims,
damages or liabilities (or actions in these respects) that arise out of or are
based upon any untrue statements or omission of necessary facts in the
information provided by the undersigned to such attorney-in-fact for purposes of
executing, acknowledging, delivering or filing Forms 3, 4 or 5 (including
amendments thereto) or Form ID and agrees to reimburse the Company and such
attorney-in-fact for any legal or other expenses reasonably incurred in
connection with investigating or defending against any such loss, claim, damage,
liability or action.

       This Power of Attorney supersedes any power of attorney previously
executed by the undersigned regarding the purposes outlined in the first
paragraph hereof ("Prior Powers of Attorney"), and the authority of the
attorneys-in-fact named in any Prior Powers of Attorney is hereby revoked.

       This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4, and 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier revoked by the undersigned in a signed writing delivered to the
foregoing attorneys-in-fact.

       IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 18th day of September, 2013.

                                   POLARIS VENTURE PARTNERS V, L.P.

                                   By: POLARIS VENTURE MANAGEMENT CO.
                                       V, L.L.C., its General Partner

                                       By: /s/ John Gannon
                                           -------------------
                                       Name: John Gannon
                                       Title: Attorney-in-fact

                                   POLARIS VENTURE PARTNERS
                                   ENTREPRENEURS' FUND V, L.P.

                                   By: POLARIS VENTURE MANAGEMENT CO.
                                       V, L.L.C., its General Partner

                                       By:  /s/ John Gannon
                                            ------------------
                                       Name: John Gannon
                                       Title: Attorney-in-fact

                                   POLARIS VENTURE PARTNERS FOUNDERS'
                                   FUND V, L.P.

                                   By: POLARIS VENTURE MANAGEMENT CO.
                                       V, L.L.C., its General Partner

                                       By:  /s/ John Gannon
                                            ------------------
                                       Name: John Gannon
                                       Title: Attorney-in-fact

                                   POLARIS VENTURE PARTNERS SPECIAL
                                   FOUNDERS' FUND V, L.P.

                                   By: POLARIS VENTURE MANAGEMENT CO.
                                       V, L.L.C., its General Partner

                                       By: /s/ John Gannon
                                           -------------------
                                       Name: John Gannon
                                       Title: Attorney-in-fact

                                   POLARIS VENTURE MANAGEMENT CO.
                                   V, L.L.C.

                                       By: /s/ John Gannon
                                           -------------------
                                       Name: John Gannon
                                       Title: Attorney-in-fact