Exhibit 24.4

                                 POWER OF ATTORNEY

    Know all by these present, that Takeda Pharma A/S, a stock limited company
incorporated under the laws of Denmark, and with business address at Langebjerg
1, 4000 Roskilde, Denmark ("Takeda Denmark"), in its capacity as a shareholder
of Molecular Templates, Inc., a Delaware company with principal offices located
at 9301 Amberglen Blvd, Suite 100, Austin, Texas 78729 (the "Company") hereby
constitutes and appoints each of Michael Broxson, Gregory Fralish, Paul Sundberg
and Brett Budzinski, signing singly, as the undersigned's true and lawful
attorney-in-fact to take the following actions related to the Company in Takeda
Denmark's capacity as a shareholder of the Company:

    (1) execute for and on behalf of Takeda Denmark, forms and authentication
        documents for EDGAR Filing Access, including without limitation a Form
        ID or any application materials to enable Takeda Denmark to gain or
        maintain access to the Electronic Data Gathering, Analysis and Retrieval
        System of the SEC;

    (2) do and perform any and all acts for and on behalf of Takeda Denmark
        which may be necessary or desirable to complete and execute any such
        forms and authentication documents;

    (3) execute for and on behalf of Takeda Denmark, in Takeda Denmark's
        capacity as a shareholder of the Company, any and all instruments,
        certificates, and documents required to be executed on behalf of Takeda
        Denmark pursuant to Section 13 and Section 16 of the Securities Exchange
        Act of 1934, as amended, and the rules thereunder (collectively, the
        "Exchange Act"), including without limitation Forms 3, 4 and 5 and
        Schedules 13D and 13G (including any amendments thereto);

    (4) do and perform any and all acts for and on behalf of Takeda Denmark
        which may be necessary or desirable to prepare, complete and execute any
        such instruments, certificates, and documents required to be executed on
        behalf of Takeda Denmark pursuant to Section 13 and Section 16 of the
        Exchange Act, prepare, complete and execute any amendment or amendments
        thereto, and file such instruments, certificates and documents with the
        U.S. Securities and Exchange Commission and any stock exchange or
        similar authority; and

    (5) 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, Takeda
        Denmark, it being understood that the documents executed by such
        attorney-in-fact on behalf of Takeda Denmark 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.

    Takeda Denmark 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 Takeda Denmark might or
could do if legal representatives of Takeda Denmark were personally present,
with full power of substitution or revocation, hereby ratifying and confirming
all that such attorney-in-fact shall lawfully do or cause to be done by virtue
of this power of attorney and the rights and powers herein granted.  Takeda
Denmark acknowledges that the foregoing attorneys-in-fact, in serving in such
capacity at the request of Takeda Denmark, are not assuming nor relieving any of
Takeda Denmark's responsibilities to comply with Section 13 or Section 16 of the
Exchange Act.  Takeda Denmark acknowledges that the foregoing attorneys-in-fact
do not assume (i) any liability for Takeda Denmark's responsibility to comply
with the requirements of the Exchange Act, (ii) any liability of Takeda Denmark
for any failure to comply with such requirements or (iii) any obligation or
liability of Takeda Denmark for profit disgorgement under Section 16(b) of the
Exchange Act.

    This Power of Attorney shall remain in full force and effect until Takeda
Denmark is no longer required to file forms and execute authentication documents
with respect to Takeda Denmark's EDGAR Filing Access or to file any instruments,
certificates and documents pursuant to Section 13 and Section 16 of the Exchange
Act with respect to Takeda Denmark's holdings of and transactions in securities
issued by the Company, unless earlier revoked by Takeda Denmark at any time at
its sole discretion.  This Power of Attorney shall expire as to any individual
attorney-in-fact if such attorney-in-fact ceases to serve as an employee of a
subsidiary of Takeda Pharmaceutical Company Limited (Japan) that is registered
in the United States.

                              [Signature page follows]


    IN WITNESS WHEREOF, Takeda Denmark has caused this Power of Attorney to
become effective as of the last date set forth below.


TAKEDA PHARMA A/S


By:    /s/ Ghita Astrup
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Name:  Ghita Astrup
     ---------------------------
Title: Managing Director
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Date:  August 25, 2017
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