Cleary hurt his ankle when he was struck by a puck shot by teammate Brad Stuart during Sunday's 4-1 victory at Minnesota, only moments after he had notched his team-best 16th goal of the year.
The Wings said Cleary's ankle won't need surgery.
It was only the latest bad injury news for Detroit. The club lost high-scoring forward Pavel Datsyuk last week with a broken hand. The Red Wings left winger, who has notched 27 assists in 33 games, will also be out for at least a month.
Forward Jan Mursak was recalled from Grand Rapids of the American Hockey League to fill Cleary's roster spot.
Celebrity Families of 2014 [PHOTOS]