Redd already had been suspended without pay for four games last season for violating the same policy, though he was on injured reserve after tearing his ACL and MCL during training camp and wasn't guaranteed to make the roster before the injury.
He was not a big factor in Washington's plans for this season before the latest news.
Washington has two experienced backs on the roster in Matt Jones and Chris Thompson and might draft a running back as well. They also remain interested in free agent Pierre Thomas, who spent the final month of the season with them.
It's a bad turn of events for Redd, who was once a ballyhooed runner at Penn State, where he rushed for 1,188 yards as a sophomore. But in the wake of the Jerry Sandusky controversy and head coach Joe Paterno's ouster, Redd transferred to Southern California.
He made the Redskins as an undrafted free agent in 2014. He rushed for 75 yards and caught eight passes for 107 more as a rookie.