Rodgers-Cromartie, in his second season, leads Arizona in interceptions with six and was selected to the Pro Bowl.
He was taken off the field on a cart with 13:23 left in the first quarter while tackling Packers tight end Jermichael Finley.
Word came several minutes later that the injury was a bruise and nothing more serious, as was first feared.
Arizona wide receiver Anquan Boldin injured his left ankle in the third quarter and left the game. Although the injury did not appear serious, he limped off the field and would not return, the team said.