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."
Lahm has featured in 18 matches for Bayern this season.
Pep Guardiola's men resume Bundesliga action on Saturday with a home game against Hoffenheim at the Allianz Arena.
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