The reigning NFL MVP was hurt when he was hit by Falcons rookie linebacker Deion Jones on an unsuccessful try for a two-point conversion.
Newton, who was 14 of 25 passing for 165 yards and a touchdown, was replaced by veteran backup Derek Anderson.
Linebacker Thomas Davis injured his left hamstring on a tackle in the third quarter.
Davis, a 12-year-veteran from the University of Georgia, attempted to play through the injury before eventually exiting the game.
Two-year veteran David Mayo replaced Davis, who was in on 10 tackles in the Panthers' first three games and had a sack.
Carolina rookie cornerback James Bradberry also left the game after injuring a toe on his left foot in the first quarter.
Fellow rookie Daryl Worley replaced Bradberry, who was taken to the dressing room after being looked by staff on the sideline.
Bradberry moved into the starting lineup after being the Panthers' second-round pick in the NFL draft out of Samford University. He was taken 62nd overall.