Mitchell underwent surgery on Monday but coach Hue Jackson said he doesn't believe the injury will end the veteran cornerback's season.
Mitchell suffered the injury on a third-down throw from Oakland Raiders quarterback Derek Carr to wide receiver Jordy Nelson in the first half of the Browns' 45-42 overtime loss. After the pass fell incomplete, he was carted off the field.
Mitchell, signed as a free agent in the offseason, had one interception and two forced fumbles in four games, and had emerged as a key defender for the Browns.
Veteran E.J. Gaines replaced Mitchell and recorded his first interception of the season against the Raiders.