The 33-year-old defenseman missed the first nine games of the season with the same illness.
Green has 26 points (five goals, 21 assists) in 43 games this season and is second on the Red Wings with an average ice time of 21:41 per game.
"The doctor has suggested several weeks of complete rest to deal with it, so he'll be out for the season," Red Wings coach Jeff Blashill said. "From what we understand, the complete rest should take care of it. This shouldn't be something that keeps coming back."
Selected by the Washington Capitals with the No. 29 pick in the 2004 NHL Draft, Green has 490 points (147 goals, 343 assists) in 830 NHL games in 14 seasons with the Capitals and Red Wings.
Dylan Larkin will not play against the New York Rangers at Little Caesars Arena on Thursday (7:30 p.m. ET; FS-D, MSG, NHL.TV) because of a back injury. He will be evaluated by a specialist, with an update expected Friday.
The 22-year-old center leads Detroit in goals (27), assists (35) and points (62).
"We should have a better idea in the next few days," Blashill said of Larkin's prognosis. "I don't think we're talking about years or anything like that, but I don't have many answers right now. We'll know after he has the tests and talks to the doctor."
The Red Wings (23-33-10) are in 15th place the Eastern Conference.
NHL.com correspondent Dave Hogg contributed to this report
