Burnett underwent surgery Tuesday with renowned foot specialist Dr. Robert Anderson and is expected to make a full recovery.
Burnett started eight games for the Browns this year, tallying 41 tackles and two sacks. He also had an interception Thursday against Pittsburgh, shortly before suffering the injury.
Burnett's injury is the latest blow to a Cleveland defense that was still without safety Eric Murray (knee) and that will remain without defensive end Myles Garrett, who was suspended for the season by the NFL last week.
Burnett, 30, was signed by the Browns in April after the Steelers waived him.