The Republic of Ireland international sustained the problem in Saturday's 1-0 loss to Manchester United with a scan showing today that he had a small tear which would keep him out of action for about four weeks.
Villa boss Alex McLeish said it was a good chance for Brad Guzan to step up whilst urging the club to come together during Given's absence.
"It is disappointing to lose Shay in such circumstances but, unfortunately, these things happen in football," Villa boss Alex McLeish told the club's official website.
"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."