Mayfield, however, said he plans to practice Thursday and is confident he'll play Sunday against the Cincinnati Bengals.
"Mama didn't raise a wuss," he said Wednesday.
Mayfield was injured just before halftime when his throwing hand collided with the facemask of Pittsburgh pass-rusher Bud Dupree. Mayfield exited for the locker room early to get X-rays, which came back negative, allowing him to finish the game while wearing a glove.
"It could've been pretty bad," Mayfield said. "Pretty fortunate."
Left tackle Greg Robinson cleared concussion protocol and returned to practice Wednesday. Robinson was sidelined for Cleveland's loss at Pittsburgh after showing up to the Browns practice facility with concussion symptoms last week.