The Ireland midfielder, who has been playing in central defence this season for United due to absentees, is believed to have suffered the injury during their season-opening 1-0 defeat by Chelsea at Stamford Bridge.
United have been battling with injuries, suspension and Olympic duties this month which have ruled out up to nine players from Alex Ferguson's squad.
"He's been playing with a bit of pain and it was just too much after Saturday," said Ferguson after his weakened team beat Dinamo Bucharest 3-0 to reach the Champions League group phase at Old Trafford on Wednesday.
"He was really feeling it. He is going to be out for three weeks which is a bit of a blow."
