Barkley, a senior, was injured during USC's 38-28 loss to UCLA Nov. 17. He missed the Trojans' final regular-season game against Notre Dame, in which the No. 1-ranked Fighting Irish wrapped up a perfect regular season with a 22-13 win.
Freshman Max Wittek replaced Barkley against Notre Dame and Kiffin said Wittek would start at quarterback in the Sun Bowl Monday against Georgia Tech.
"I've worked as hard as I could to get back for this game and nature is not allowing it," Barkley said Thursday.
Barkley is considered one of the top quarterback prospects heading into the 2013 NFL draft.
Celebrity Families of 2014 [PHOTOS]