Weimann limped off with the problem just before the hour mark of Saturday's goalless draw at West Ham and is now a major doubt for the clash with the Blubirds.
"It looks like a hamstring at the minute. I don't know how severe it is," Villa manager Paul Lambert told the club's official website.
"The thing is we've one more game then we get a break, so hopefully the break helps him."
Midfielder Fabian Delph, meanwhile, should be available after missing the game at Upton Park through sickness.
"He pulled out of training on Thursday. He came in on Friday, but he still didn't look the greatest so we sent him home," added Lambert.
"There's been a bug going around. Ciaran (Clark) had it the other week, so hopefully Fabian will be all right for the next game."