The possibility was first reported by SportsLine.com's Dennis Dodd on Monday morning.
South Carolina athletic director Mike McGee said the Gamecocks' actions on the field were not consistent with the values and ethics of the school.
"This decision will have a significant financial impact on USC athletics. We will also lose a month of prebowl practice," McGee said. "It was a decision that had to be made."
Clemson athletics director Terry Don Phillips said in a statement the decision isn't fair to the majority of the players.
|Clemson's Yusef Kelly kicks a South Carolina player in the head during the brawl.(AP)|
Both teams qualified for the postseason with 6-5 records.
The brawl, which broke out with about six minutes left in the game, started when Tigers defensive lineman Bobby Williamson took down South Carolina quarterback Syvelle Newton and appeared to linger too long on top of him.
South Carolina coach Lou Holtz, in his last game after a 33-year career, and Clemson coach Tommy Bowden tried to break up the brawl. Eventually, security and police officers were needed to restore order. Clemson won 29-7.
McGee said individual suspensions for players will be forthcoming.