Stephenson was suspended for violating the league's substance abuse policy. He will miss games at home against Pittsburgh and at New Orleans. He can participate in all offseason and preseason practices and games.
Stephenson was not in attendance at the team's minicamp this week, and coach Hue Jackson said Stephenson would be fined for his absence. ProFootballTalk.com reported his fines for missing minicamp would total $84,435. He also had not been seen at the recent OTA practices open to the media.
Stephenson played in Kansas City from 2012 through 2015, then in Denver the past two seasons. In March, he signed a one-year, $2.5 million deal to join the Browns.
Stephenson has started 37 games in his five NFL season. His role with the Browns remains to be determined, though he can play both tackle spots.