Vlaar was forced off with the problem during the first half of Villa???s goalless draw with Crystal Palace on New Year???s Day.
The 29-year-old Netherlands international previously underwent cruciate ligament surgery twice during his time with Feyenoord and has missed several games this season due to a knee problem picked up at the World Cup in the summer.
Vlaar, who is out of contract at the end of the season, has been linked with Premier League clubs Manchester United, Arsenal and Liverpool.
However, any January move is likely to be scuppered by the news that the defender is now out of action with yet another knee injury.