Green will have surgery on his cervical spine April 5 and will need at least two months to recover. The 32-year-old, who played in the 2018 Honda NHL All-Star Game, can become an unrestricted free agent July 1.
He has 33 points (eight goals, 25 assists) in 66 games and missed seven games from Feb. 17-28 with a neck injury. He aggravated the injury in practice Wednesday.
The Red Wings (27-35-11) were 17 points behind the New Jersey Devils for the second wild card into the Stanley Cup Playoffs from the Eastern Conference. Detroit has nine games remaining.