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
"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."