POWER OF ATTORNEY
                       For Executing Forms 3, 4 and 5

        Know all by these presents, that the undersigned hereby constitutes and
appoints each of Steven Nichtberger, M.D., Anup Marda and Michael Gerard, each
acting singly, his true and lawful attorney-in-fact from June 1, 2022 to:

    (1) Execute for and on behalf of the undersigned, in the undersigned's
capacity as an officer, director and/or 10% shareholder of Cabaletta Bio, Inc.
(the "Company"), 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 the Company, Forms
3, 4 and 5 in accordance with Section 16(a) of the Securities Exchange Act of
1934 and the rules thereunder;

    (3) do and perform any and all acts for and on behalf of the undersigned
that may be necessary or desirable to complete the execution of any such Form
3, 4 or 5, complete and execute any amendment or amendments thereto, and the
timely filing of such form with the United States Securities and Exchange
Commission and any other authority; and

    (4) 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 interests 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
his discretion.

    The undersigned hereby grants to each such attorney-in-fact full power and
authority to do and perform all and every act and thing whatsoever requisite,
necessary, and proper to be done in the exercise of any of the rights and
powers herein granted, as fully for all intents and purposes as the such
attorney-in-fact 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 his 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
any of the undersigned's responsibilities to comply with Section 16 of the
Securities Exchange Act of 1934, as amended.

    This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required 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.

    By this Power of Attorney, the undersigned further revokes all previous
powers of attorney relating to the undersigned's obligations to file Forms 3, 4
and 5 in respect of the Company's securities under Section 16(a) of the
Securities Exchange Act of 1934 and related matters.

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

                                   /s/ Mark Simon
                                   -------------------------------
                                   Name: Mark Simon, MBA