Landry suffered the injury on the opening drive Sunday against the Houston Texans. After catching a 9-yard pass on Cleveland's first play, he left the field and did not return to the game, which the Browns won 31-21.
Landry has missed only one game since his career began in 2014. He was held out last season against the New York Jets after being deemed a close contact to someone who tested positive for COVID-19.
So far this season, Landry has 80 yards receiving, catching all his six of his targets. He also had a touchdown run in the opener against the Kansas City Chiefs.
Cleveland faces the Chicago Bears on Sunday.