Exhibit 24

                            LIMITED POWER OF ATTORNEY

        The undersigned hereby constitutes and appoints each of John Daniel
Quisel, Joanne Bryce and Rahul Khara, signing singly, and with full power of
substitution, 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 officer and/or director of Disc Medicine, Inc. (the
"Company"), from time to time the following U.S. Securities and Exchange
Commission ("SEC") forms: (i) Form ID, including any attached documents (such
as Update Passphrase Authentication), to effect the assignment of codes to the
undersigned to be used in the transmission of information to the SEC using the
EDGAR System; (ii) Form 3, Initial Statement of Beneficial Ownership of
Securities, including any attached documents; (iii) Form 4, Statement of
Changes in Beneficial Ownership of Securities, including any attached
documents; (iv) Form 5, Annual Statement of Beneficial Ownership of Securities
in accordance with Section 16(a) of the Securities Exchange Act of 1934, as
amended, and the rules thereunder, including any attached documents; (v)
Schedules 13D and 13G; and (vi) amendments of each thereof, in accordance with
the Securities Exchange Act of 1934, as amended, and the rules thereunder,
including any attached documents;

        (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 Form 3, 4 or 5, Schedule 13D or 13G, or any amendment(s) thereto and
timely file such form(s) with the SEC and any securities exchange, national
association 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, acting
singly, 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 or Regulation 13D-G of
the Securities Exchange Act of 1934, as amended. The undersigned hereby agrees
to indemnify the attorneys-in-fact and the Company from and against any demand,
damage, loss, cost or expense arising from any false or misleading information
provided by the undersigned to the attorneys-in-fact.

        This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file such forms 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. This Power of Attorney supersedes any prior power
of attorney in connection with the undersigned's capacity as an officer and/or
director of the Company. This Power of Attorney shall expire as to any
individual attorney-in-fact if such attorney-in-fact ceases to be an employee
of the Company.

        IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney
to be executed as of January 3, 2023.

                                   /s/Brian MacDonald
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                                   Signature


                                   Brian MacDonald
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                                   Print Name