South Carolina coach Steve Spurrier said after the game that Shaw is out two to three weeks.
"Hopefully in two weeks, he'll be back ready to go," Spurrier said. "He didn't see that guy. He ran the option to the right, cut back and he fumbled on the play, too. He'll get a lot of treatment."
Shaw was scrambling for a first down when he got hit and fumbled. He got up grabbing his shoulder and was immediately taken to the locker room.
Shaw returned to the field with his arm in a sling and ice on his shoulder with his pads off. Dylan Thompson replaced Shaw in the lineup.
Thompson, who finished 15 of 32 for 261 yards, one interception and a rushing touchdown, has seen extensive time as the Gamecocks' quarterback throughout his career, and has now played in three of four games this year.
Spurrier also said running back Brandon Wilds is expected to miss two to three weeks after dislocating his elbow.