Stressing the operation was "minor surgery", the club said Bradshaw has been unable to increase his running intensity without some knee discomfort.
"The operation will release his ITB (iliotibial band) to allow more flexibility in his lateral knee cap joint, and he will also have a screw removed that was inserted as part of a knee reconstruction in 2007," the statement said.
It's another blow to the Swans forward who was restricted to just nine games following knee and hamstring injuries last season after moving across from the Brisbane Lions at the start of the year.
Bradshaw, yet to play a match this season, is expected to resume running in approximately three weeks.
