The team announced the diagnosis Tuesday. Ward had an MRI on Monday, which revealed the injury.
The Browns are already without their other starting cornerback, Greedy Williams, who has yet to play a down this season and is on injured reserve due to a shoulder injury suffered in training camp.
To replace Ward in the lineup, Cleveland's options include preseason waiver pickup M.J. Stewart, nickelback Kevin Johnson, special-teams ace Tavierre Thomas, undrafted rookie A.J. Green or reserve Robert Jackson.
The Browns (7-3) will visit the Jacksonville Jaguars (1-9) on Sunday.