The move comes one day after coach Zac Taylor said the veteran lineman missed practice because of an internal discipline issue.
Taylor declined to confirm or deny a report that Glenn got into a verbal altercation with a member of the Bengals' coaching staff over his return from a concussion. According to ProFootballTalk.com, Glenn was fined $200,000 for conduct detrimental to the team and claimed he was rushed back from the injury.
After he cleared the league's concussion protocol, Glenn was a full participant at Wednesday's practice for the first time since Cincinnati's second preseason game on Aug. 15. He has not spoken publicly since the injury.
In a statement announcing the move, the team said it will not be issuing any further comment on Glenn's suspension.