Smith is suffering from a shoulder ailment, while Brown has a knee injury.
In 14 games this season, including four starts, Smith caught 14 passes for 131 yards and one touchdown. Brown recorded five tackles and a sack in 10 games.
The Browns replaced the duo on the roster by signing free agent tight end Dan Gronkowski and promoting linebacker Brian Smith from the practice squad. The team also signed wide receiver Torrey Grissett and linebacker Craig Robertson to the practice squad.