POWER OF ATTORNEY

        Know all by these present, that the undersigned hereby constitutes and
appoints each of Jason Kim, Barbara Ruskin and Megan Filoon of Molecular
Templates, Inc. (the "Company") and Matthew J. Gardella, Christina S. Bailey,
Nishant M. Dharia, Anne Leland, Brenda Meyette and Jacquelyn Cannata 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.

                    /s/ Roger J. Waltzman, MD, MBA
                    ------------------------------
                    Name: Roger J. Waltzman, MD, MBA
                    Date: 24th January, 2019