It is expected the 73-gamer will return to team training in February.
Swans Head of Football Charlie Gardiner says he expects Menzel to recover well.
“It’s been well documented that Dan had some issues with his groin this year so we wanted to get on top of it now rather than it potentially become an issue during next season,” Gardiner.
“The medical team identified an opportunity to potentially improve Dan's output and his durability longer term. The surgery was performed last week, which went well.
“We know Dan is a real professional who will do everything required in his rehab and we're confident he'll make a successful return to training in February.”