The Browns noted Stephenson is eligible to participate in offseason practices, training camp and preseason games, but he'll miss the first two weeks of the 2018 regular season.
Stephenson, who signed with Cleveland in March after spending the last two years with the Denver Broncos, wasn't in attendance for the team's minicamp this week and head coach Hue Jackson hinted there could be news on the horizon.
"That will all come to an end here pretty soon," Jackson told reporters. "Obviously, the guy is not here for minicamp. There are fines involved. There are all of those things that we will deal with. At this time, I only want to talk about the guys that are here and working and doing the things that they need to be doing right now."
The 29-year-old Missouri native played the first four seasons of his career with the Kansas City Chiefs, who selected him in the third round of the 2012 draft.
Shon Coleman and Chris Hubbard are the Browns' projected starters at tackle heading toward training camp. They could receive competition from Austin Corbett. Friday's news means Stephenson likely won't get many snaps with the first-team offense during the preseason.
He'll miss games against the Pittsburgh Steelers and New Orleans Saints before becoming eligible to return for a Week 3 clash with the New York Jets.