LIMITED POWER OF ATTORNEY

The undersigned hereby constitutes and appoints Edward Albini, Regina Cheng,
Linda Fitzpatrick and David Pauling, as long as they are providing services to
Sutro Biopharma, Inc., a Delaware corporation (the "Company"), or any of them,
the undersigned's true and lawful attorney-in-fact to:

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

(2)	do and perform any and all acts for and on behalf of the undersigned that
may be necessary or desirable to complete and execute any such Forms 3, 4s and
5s and timely file such forms with the Securities and Exchange Commission and
any stock exchange or similar authority, if required; and

(3)	take any other action of any type whatsoever in connection with the
foregoing that, 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 each 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 and revocation,
hereby ratifying and confirming all that each such attorney-in-fact, or each
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 each of the foregoing
attorneys-in-fact, in serving in such capacity at the request of the
undersigned, is not assuming, nor is the Company assuming, any of the
undersigned's responsibilities to comply with Section 16 of the Exchange Act.

The undersigned agrees that each such attorney-in-fact may rely entirely on
information furnished orally or in writing by the undersigned to each 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 on
any untrue statement or omission of necessary facts in the information provided
by the undersigned to such attorney-in-fact for purposes of executing,
acknowledging, delivering and filing Forms 3, 4s or 5s (including amendments
thereto) and agrees to reimburse the Company and each 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 shall remain in full force and effect until the
undersigned is no longer required to file Forms 3, 4s and 5s 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 April 20, 2023.

/s/ Venkatesh Srinivasan
Name:  Venkatesh Srinivasan