The Bulgarian midfielder sustained the problem in the first half of Saturday's defeat at Sunderland and had to come off five minutes before half-time.
And boss Gerard Houllier has confirmed the injury is serious enough to keep the 31-year-old out for upto eight weeks, with a scan planned later this week to determine whether he needs surgery.
"We have lost Stiliyan Petrov for maybe two months," Houllier told Sky Sports News.
"We will know whether he needs an operation by the middle of the week.
"It's a shame because he was getting back to a good level."
Meanwhile, Villa held an open training session at Villa Park ahead of their Carling Cup clash with Burnley and Houllier paid tribute to the 10,000 fans that braved the freezing conditions to turn up.
"It shows that there is a real community at the club and I thought that in my first home game against Chelsea, the support was magnificent.
"This is one of the reasons why I came here because of the fans. It's a good club with a good fanbase."