The Red Wings announced the move Saturday, a day after beating Buffalo to strengthen their position as a wild-card team in the playoffs.
Glendenning has no goals and six assists in 51 games this season as a rookie. With 78 hits and 32 blocked shots, he has earned ice time this season for a team that has been hit hard by injuries.
The 24-year-old Glendening was not drafted after playing at Michigan, where he walked on the team. He went on to play for the Providence Bruins in the American Hockey League and the Toledo Walleye in the East Coast Hockey League. Glendening started this season with his hometown Grand Rapids Griffins in the AHL.