Stoner suffered torn ligaments and fractures to his ankle, tibia and fibula in a practice accident in Indianapolis 12 days ago.
Although the Repsol Honda rider went on to finish fourth in that race, he missed Sunday's event in Brno on doctor's advice.
Following the surgery a statement from Honda Racing Corporation said: "Today [Thursday] in Australia, Repsol Honda's Casey Stoner received surgery to his ankle.
"Doctors are pleased with how the operation went, and now must wait during this initial recuperation period to see how the ankle is healing."
The injury has ended the 26-year-old's hopes of winning a third world title prior to his retirement at the end of the year.