The Austrian suffered the injury during Villa's 0-0 draw with West Ham United at Upton Park on Saturday afternoon.
Although there is no indication as to how long the 22-year-old will be out of action for, it is expected that he will miss next weekend's clash against Cardiff City.
"It looks like a hamstring at the minute. I don't know how severe it is," said Villa manager Paul Lambert.
Weimann has made 11 appearances in all competitions so far this term.