Bayern claim he has subsequently sustained a foot injury in training ahead of Saturday's game with Augsburg at the Allianz Arena.
A Bayern statement read: "Manuel Neuer underwent a successful minor operation by Prof Dr Markus Walther on Wednesday evening after sustaining an injury to his left foot in training.
"The 31-year-old Germany keeper will be sidelined for FC Bayern's Bundesliga matches against Augsburg on Saturday and Hoffenheim next Tuesday."
That would clear Neuer – who has not missed a top-flight game since 2015 – to return for the visit of Borussia Dortmund on April 8.
Carlo Ancelotti's side sit 13 points clear at the summit of the Bundesliga with just nine games remaining.