Bradford was pushed out of bounds as he tried to run to the sideline after scrambling, but he fell awkwardly on his knees and remaining down on the sideline for several minutes. He was helped to his feet by the St. Louis training staff before being carted to the locker room. There is no further update on his status at this time.
There was no flag on the play, as it was a clean hit, but members of the Rams' offensive line took exception to the celebration of Panthers' defensive back Mike Mitchell, who was unaware of the injury. Sunday's game has become a chippy one from both sides, with a lot of pushing and shoving as well as an ejection for defensive end Chris Long, which happened in the third quarter.
There is no indication on the severity of Bradford's injury, but he was in a lot of pain and appeared unable to stand on his own.
Here's a GIF of how and when the injury occurred, via Daniel Doelling: