The team initially thought Quinn only bruised his hand after banging it on the helmet of a Bills player. But after he complained of soreness following Wednesday's practice, X-rays were taken and revealed a fracture on the tip of his finger.
Quinn was cleared to play by a specialist at the Cleveland Clinic.
"We plan to monitor him on a regular basis, just to make sure that it's not getting worse or anything like that," Browns coach Romeo Crennel said Thursday. "But he's going to play, he's going to practice, he's going to try to help the team win."
Making his second career start and first on the road, Quinn stayed in against Buffalo and finished 14-of-36 for 185 yards. Late in the fourth quarter, he completed passes of 12 and 16 yards to set up Phil Dawson's winning 56-yard field goal with 1:39 left.
Before practice on Thursday, Quinn said his throwing hand was hit in the first and second quarters. He was surprised to learn it was broken.
"At this point, it's just a little sore," he said. "I practiced yesterday, practicing today. Just doing the best we can to take all the precautions to make sure it's all right."
Quinn, who recently replaced Derek Anderson as Cleveland's starter, didn't seem bothered while throwing the ball during the first 30 minutes of practice that are open to the media.
Quinn will wear a splint on his finger when he is not on the field.