Chester was forced off late in the first half at Villa Park and now faces a race against time to recover for the Wembley showpiece on May 17.
Although Chester is not being fully ruled out, manager Steve Bruce said he would be "amazed" if the centre-back returned to action in time.
"It's a big blow," said Bruce after the match at Villa Park. "We're not going to rule him out but it doesn't look very good. It is really, really cruel for him."
Paul McShane and Allan McGregor may yet return in time for the final with Irish defender McShane playing in a behind-closed-doors game at Leeds on Friday while McGregor is waiting for the all-clear from specialists following his recent kidney problems.
Bruce said the defeat at Villa was City's worst performance of the season.
"We made too many mistakes," he said. "When you make mistakes and don't defend properly and don't have a resilience about you, then you're going to have afternoons like this in the Premier League."
He also admitted Cup final fever has had an effect on his side.
"I've said for the last couple of weeks we have to keep focused," he said.
"The whole city is talking about the FA Cup final and why shouldn't it be? But it's been very, very difficult to keep a lid on it when we've still got a little bit of work to do.
"It's at the forefront of everybody's mind and that's only human nature because it's something we're all looking forward to."