POWER OF ATTORNEY

        KNOW ALL BY THESE PRESENTS, that the undersigned hereby constitutes and
appoints each of (i) the President and Chief Executive Officer of Aimmune
Therapeutics, Inc., a Delaware corporation (the "Company"), who is currently
Stephen G. Dilly or (ii) the Company's General Counsel and Corporate Secretary,
who is currently Douglas T. Sheehy, and their respective successors, signing
singly, with full power of substitution, as 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 a director of the Company, Forms 3, 4 and 5 (including
amendments thereto) in accordance with Section 16(a) of the Securities Exchange
Act of 1934 and the rules and regulations thereunder and a Form ID, Uniform
Application for Access Codes to File on EDGAR;

        (2)     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 3, 4 or 5 or Form ID and timely file such forms (including amendments
thereto) and application with the United States Securities and Exchange
Commission and any stock exchange or similar authority; and

        (3)     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 or 5 with respect to the
undersigned's holdings of and transactions in securities issued by the Company,
unless earlier (a) revoked by the undersigned in a signed writing delivered to
the foregoing attorneys-in-fact or (b) superseded by a new power of attorney
regarding the purposes outlined in the first paragraph hereof dated as of a
later date.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to
be executed as of this 13th day of March, 2017.

                                        /s/ Kathryn E. Falberg
                                        ---------------------------------------
                                        KATHRYN E. FALBERG