Jones picked up the injury in training for the Red Devils, and has not played for the Old Trafford club this season having also picked up a back problem during their pre-season tour.
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In a statement to their official website, a club spokesman said: "Phil Jones has had surgery on a knee meniscus tear sustained in training that will require six to eight weeks of rehabilitation."
Jones joined United in the summer of 2011 from Blackburn Rovers for a fee believed to be around £16.5 million, making his debut in the Community Shield against Manchester City.
He made 29 appearances for the club in the Premier League as they finished second behind their city rivals, scoring his first goal for the club against Aston Villa.
Last season, Jones made his debut for the England senior side in the 2-2 draw away to Montenegro in their Euro 2012 qualifier, and was included in manager Roy Hodgson's final squad for the tournament.
The Red Devils still have other injury concerns in their defence, as Chris Smalling remains unavailable with a broken metatarsal, but Jonny Evans and Rio Ferdinand have recently returned to the squad, with Ferdinand starting in their last game against Southampton.