Brown, a junior who started five games last season, suffered the injury Tuesday night in a non-contact drill.
"I feel terrible for C.J.," coach Randy Edsall said in a statement. "He's worked incredibly hard to be the starting quarterback of this team. He's stepped up and been a tremendous leader. We'll do everything we can to make sure he gets the best treatment to help in his recovery."
The transfer of former starter Danny O'Brien to Wisconsin has left the position extremely thin and inexperienced. The injury to Brown is a huge blow to a team trying to rebound from a 2-10 season. No other quarterback on the roster has thrown a collegiate pass.
"Although C.J. won't be out on the field, he'll continue to be an important part of this program," Edsall said. "As a captain and team leader, he'll do everything he can to help mentor the other quarterbacks on our team."