Jerome Boateng has not played since a shaky display in the 3-2 Champions League defeat at Rostov on November 23 and went under the knife in Munich on Tuesday.
The operation was deemed a success with Bayern suggesting the Germany international will be sidelined until early February.
A club statement read: “Prof. Dr. Andreas Imhoff operated on the right pectoral muscle of Jerome Boateng on Tuesday in Munich.”
Bayern doctor Volker Braun added: “The operation went very well. If the healing process is optimal, Jerome Boateng will not be available for about six weeks.”
The 28-year-old has suffered another injury-plagued season, making just 14 appearances for club and country due to knee and hamstring problems.
He will spend the mid-season break working on his rehabilitation, although he is unlikely to be fit when Bayern resume their Bundesliga campaign at Freiburg on January 20.