McCown kept playing despite taking a big hit in the second half, but had to leave the field after throwing an incompletion in the fourth quarter.
Coach Mike Pettine said McCown will not need surgery, but described his injury as "the worst-possible scenario."
McCown has played with several injuries during his first season with the Browns, who signed him to a three-year deal in February. He sustained a concussion while diving toward the end zone on Cleveland’s first drive this season. The 36-year-old missed two more games with injured ribs.
Pettine is not ready to announce who will replace McCown. Austin Davis came in for McCown and threw a game-tying touchdown pass. Pettine could also go back to Johnny Manziel, who was recently benched.