The 35-year-old picked up the injury in Villa’s 1-0 defeat to Manchester United on Saturday.
Villa manager Alex McLeish told the club’s official website: “It is disappointing to lose Shay in such circumstances but, unfortunately, these things happen in football.
“We have to meet these challenges and we will. We have total faith in Brad who, as I said after the game against Manchester United on Saturday, can be proud of the way he stepped in when Shay had to come off.
“We will need within the football club for everybody to stick together and that strength of unity will help massively.”
