Landry has a sprained MCL, further testing revealed Monday, a source told ESPN's Jeremy Fowler.
Landry caught a 9-yard pass on Cleveland's first snap but then left the field and did not return to the game, which the Browns won 31-21.
The Browns were already without wide receiver Odell Beckham Jr., who has yet to play this season as he returns from last year's knee surgery.
Rashard Higgins replaced Landry in the lineup.
The Browns had another injury scare in the first half when quarterback Baker Mayfield took a shot to his left shoulder while trying to make a tackle after throwing an interception. He briefly went to the locker room but returned in time for Cleveland's next possession and later scored on a 5-yard touchdown run just before halftime.