Vorm hurt himself stretching to stop Carlos Tevez's shot for the only goal of the game at the Etihad Stadium and left the field on a stretcher.
Manager Michael Laudrup confirmed after the match that the Dutchman was now facing a spell on the sidelines.
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."
Vorm received lengthy treatment on the field after suffering the injury just after the hour and was replaced by Gerhard Tremmel.
Laudrup said: "Now Gerhard has to be ready, starting with the Liverpool and Chelsea games."