
The 22-year-old, who has scored seven goals in his last seven games, could miss up to four English Premier League games and one Champions League game.
But he is definitely out of England's final Euro 2008 qualifier at home to Croatia on November 21.
"It's hugely disappointing," England coach Steve McClaren said.
"Given the form he has been in and the contribution he has made to England over the last two games means it is a blow. But we have to deal with it, like we have dealt with situations like these before.
"It is an opportunity for someone else to come and do a job."
Rooney missed five matches at the start of the season because of a broken foot but returned to form of late, helping United move alongside Arsenal at the top of the league.
United striker Louis Saha, who has only just returned from injury himself, is now likely to be called into action for United.
Peter Crouch is the most likely replacement for Rooney in the England side alongside definite starter Michael Owen.