The team announced the roster move Tuesday. Burnett started eight games for the Browns this season and recorded 41 total tackles, two passes defensed and two sacks.
Burnett also had an interception during Thursday's matchup against the Pittsburgh Steelers, shortly before he sustained the Achilles injury in the second quarter.
Burnett's injury is the latest setback to a Browns defense that is without safety Eric Murray (knee) and star defensive end Myles Garrett, who was suspended for the remainder of the season by the NFL last week.
The Green Bay Packers originally selected Burnett in the third round of the 2010 NFL Draft out of Georgia Tech. He played eight seasons with the team before signing with the Steelers in March 2018 as a free agent.
The Browns signed Burnett, 30, in April after the Steelers released him this past off-season. In 121 career games, he has tallied 770 combined tackles, 10 interceptions, 9.5 sacks and 52 pass breakups.