Bradford, 25, in his fourth NFL season, was injured Sunday during the Rams' loss to Carolina. Subsequent examinations Monday confirmed the ligament damage, the team said.
Bradford was pushed out of bounds on a fourth quarter play and was able to walk off the field but was later taken to the locker room on a cart.
He completed 159-of-262 passes for 1,687 yards and 14 touchdowns this season. He's also been intercepted four times.
The Rams made Bradford the No. 1 overall draft choice in 2010 and he's been the team's starting quarterback since. In 49 NFL games, Bradford is 1,032-of-1,760 passing for 11,065 yards and 59 touchdowns.
The Rams have just two quarterbacks on their roster -- Bradford and Kellen Clemens, who has started 12 games in his eight-season NFL career.