"The Swans had hoped the Dutch keeper would battle through until January, but after suffering more problems against Norwich City last Sunday, it was decided that the injury could not be managed any longer," the club said on their website (www.swanseacity.net).
The length of time Vorm will be sidelined will not be clear until after the operation.
Vorm, who has played 14 times for the Netherlands, is likely to be replaced by German Gerhard Tremmel in Swansea's starting line-up.
The Welsh club, who play Everton on Sunday, also said Leon Britton and Chico Flores are expected to return to training this week after injury lay-offs.
Britton missed the last five matches with a broken toe while Flores, who was suspended for the Norwich match, hurt his knee in a Europa League match with St Gallen.