Lahm sustained the injury in a training session on Tuesday, the 31-year-old World Cup winner collapsing to the ground unchallenged.
The Bavarian club duly revealed that Lahm was facing a three-month lay-off.
And the versatile former Germany captain, who can operate as either a defensive midfielder or a full-back, has now gone under the knife.
Bayern posted on their official Twitter account: "Philipp #Lahm's operation was a success. Ankle held in place with metal plate and screws. Several weeks rest and then he begins rehab."
Pep Guardiola's men resume Bundesliga action on Saturday with a home game against Hoffenheim at the Allianz Arena.
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