POWER OF ATTORNEY

     The undersigned, as a Section 16 reporting person of Hyperion Therapeutics,
Inc. (the "Company"), hereby constitutes and appoints Lesley Calhoun, Sally
Brammell, Ashley Gould and Daniel Stellenberg as the undersigned's true and
lawful attorneys-in-fact to:

     1.    complete and execute Forms 3, 4 and 5 and other forms and all
           amendments thereto as such attorneys-in-fact shall in their
           discretion determine to be required or advisable pursuant to Section
           16 of the Securities Exchange Act of 1934, as amended, and the rules
           and regulations promulgated thereunder, or any successor laws and
           regulations, as a consequence of the undersigned's ownership,
           acquisition or disposition of securities of the Company; and

     2.    do all acts necessary in order to file such forms with the Securities
           and Exchange Commission, any securities exchange or national
           association, the Company and such other person or agency as the
           attorneys-in-fact shall deem appropriate.

      The undersigned hereby ratifies and confirms all that said attorneys-in-
fact and agents shall do or cause to be done by virtue hereof. 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, as amended.

     This Power of Attorney shall remain in full force and effect until the
undersigned is no longer required to file Forms 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
Company and the foregoing attorneys-in-fact.

     IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be
executed as of this 5th day of May, 2015.

                                            Signature:

                                            /s/ James I. Healy
                                            -------------------------------
                                            Name: James I. Healy

                                            Sofinnova Venture Partners VII, L.P.
                                            By: Sofinnova Management VII, LLC
                                            Its General Partner

                                            By: /s/ James I. Healy
                                                ---------------------------
                                            James. Healy, Managing Member