Vorm has missed the last five games and will be unavailable for this weekend's Barclays Premier League clash against Manchester United at Old Trafford.
But the 30-year-old Dutchman, who has kept seven clean sheets in 17 appearances for the Swans this season, is on the road to recovery.
"The operation went to plan," Vorm told the club's official website.
"There was a little tear in my meniscus, which caused a lot of problems, but a small operation of around 30 minutes sorted things out.
"After a week of the operation, I feel much better than before. I can do almost everything already.
"My knee has a little bit of fluid in it, which is normal at this stage, but I'm very comfortable with my recovery. My knee feels better and my movement has improved, so that's great for me."
Vorm, though, will not rush his comeback as Gerhard Tremmel continues between the posts for Swansea.
"The good thing is that I won't be rushing myself back," Vorm added.
"I need to take my time and make sure I am 100 per cent before I put myself forward for potential selection.
"I've not said to myself that I should make it back for this game or a certain date, because in a way that can affect you if you don't make it back by then.
"I just want to make sure everything is perfect before I am back on the pitch."