Norwood suffered the injury late in the first half when he hit the ground hard after battling cornerback Montel Garner to make an 11-yard catch.
Norwood was helped to the bench and eventually carted to the locker room.
The third-year wide receiver, who was Carolina acquired in a trade with the Seattle Seahawks prior to the start of the 2015 season, has been competing for one of the final spots on the active roster. He played in just one game last year and did not record a catch.