The Dutchman injured his groin attempting to save Carlos Tevez's winning goal for Manchester City at the Etihad.
And Swansea manager Michael Laudrup revealed after the 1-0 defeat that Vorm will be missing for at least month.
He said: Laudrup said: "It is his groin, so we are talking four to six weeks.
"But that's a part of football, that is what can happen in December, January with the weather, the accumulation of games. That's a part of it."
Gerhard Tremmel came on for Vorm at City and will now start at Liverpool in the Capital One Cup ahead of next week's home game against Chelsea.
Laudrup said: "Now Gerhard has to be ready, starting with the Liverpool and Chelsea games."
Swansea were the better side for long spells, but Michu twice failed to beat Joe Hart with good chances and Laudrup said: "We have to say, both times, Joe Hart made great saves.
"Playing against the champions away, when they only create one clear chance in 90 minutes and you create two or three, you can think you deserved a little more.
"The great teams just take those few chances and convert them into goals. I want to only see the positive things because there are so many."
Laudrup's one gripe was Angel Rangel's yellow card for diving which means a one-match ban.
He said: "Angel got a fifth yellow card - that was really something, that was something special. I have to admit that.
"A free-kick against and it was strange. If that is diving, then we have invented a new form of diving. I have to ask Angel how he learned that."