Grant had to be carted off the field during Tuesday's practice after suffering the injury in the drill. A source said the team is awaiting imaging to confirm the Achilles tear.
The Browns signed Grant to a three-year deal this offseason to be their kick and punt returner; Grant, however, was also having a standout training camp as a receiver out of the slot, as well.
Earlier this week, Browns special teams coordinator Mike Priefer said he thought Grant would "transform" Cleveland's return game.
If Grant is out, the Browns will likely turn to Demetric Felton to return punts and kicks for them.