The veteran Welshman suffered the injury in a collision with Steve Sidwell during the second half of the 1-1 draw and left Villa Park with his arm in a sling.
Manager Sir Alex Ferguson revealed the 36-year-old had been sent for an x-ray and hoped the news would be good. Instead, the Old Trafford outfit have confirmed Giggs will be sidelined for a period that includes both legs of the Champions League last-16 clash with AC Milan plus the Carling Cup final with Villa at Wembley on February 28.
Apart from those high-profile fixtures, Giggs will also miss Premier League games against Everton, West Ham and Wolves.