POWER OF ATTORNEY

     Know all by these present, that the undersigned hereby constitutes and
appoints each of Jason Kim, President, Chief Operating Officer and Principal
Financial Officer of Molecular Templates, Inc. (the "Company"), and Matthew
Gardella, Matthew Tikonoff, Nishant Dharia, Adam Davey, Jacqueline Cannata, Anne
Leland and Brenda Meyette of Mintz, Levin, Cohn, Ferris, Glovsky and Popeo,
P.C., signing singly, with full power of substitution, the undersigned's true
and lawful attorney-in-fact to:

     (1) execute for and on behalf of the undersigned, forms and authentication
         documents for EDGAR Filing Access;

     (2) execute for and on behalf of the undersigned, in the undersigned's
         capacity as an officer, director and/or 10% shareholder of Company,
         forms and authentication documents for EDGAR Filing Access;

     (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
         forms and authentication documents;

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

     (5) 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, prepare, complete and execute any amendment or
         amendments thereto, and timely file such form with the U.S. Securities
         and Exchange Commission and any stock exchange or similar authority;
         and

     (6) 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
relieving, nor is the Company assuming nor relieving, any of the undersigned's
responsibilities to comply with Section 16 of the Exchange Act.  The undersigned
acknowledges that neither the Company nor the foregoing attorneys-in-fact assume
(i) any liability for the undersigned's responsibility to comply with the
requirements of the Exchange Act, (ii) any liability of the undersigned for any
failure to comply with such requirements or (iii) any obligation or liability of
the undersigned for profit disgorgement under Section 16(b) of the Exchange Act.

     This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file forms and execute authentication
documents with respect to the undersigned's EDGAR Filing Access or 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.

                            [Signature page follows]

     IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of the date set forth below.


                          Signature: /s/ Harold E. Selick
                                     --------------------

                          Name:  Harold E. Selick
                                 ----------------

                          Date: 7/28/2017
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