Browns head coach Mike Pettine said Austin has been a model player during his first season in Cleveland.
"Miles sustained a kidney injury in Buffalo and remains in the hospital. Our thoughts are with him and we wish him a speedy recovery. Miles is a guy who embodies what 'Play like a Brown' means and instills that in our receiving corps."
Prior to the injury, Austin appeared in 12 games and he had 47 receptions for 568 receiving yards and two touchdowns.
Browns receiver Josh Gordon returned from suspension two weeks ago and will start alongside Andrew Hawkins moving forward. In two games this season, Gordon has 15 catches for 195 yards, while Hawkins has 52 catches for 718 yards and two touchdowns in 11 games.
Cleveland is No. 12 in passing yards and No. 30 in passing touchdowns this season.
The Browns are 7-5 and tied with the Baltimore Ravens and Pittsburgh Steelers for second place in the AFC North. They host the Indianapolis Colts on Sunday at 1 p.m.