Burleson, who had been dealing with a lingering hamstring issue, only played in one preseason game. He caught one pass on two targets for 27 yards in the preseason finale.
The 32-year-old had 461 yards and one touchdown last season for the Detroit Lions.
Cornerback Isaiah Trufant was placed on injured reserve with a knee injury that forced him to miss three of the Browns' four preseason games.
Information from ESPN's Adam Schefter and Adam Caplan and ESPN.com's Pat McManamon was used in this report.