Bayern said in a statement that the 31-year-old had suffered a "repeat hairline fracture of the metatarsal in his left foot" during a training session on Monday.
He underwent surgery early on Tuesday which involved setting the fracture with a plate, the club added. Neuer suffered a similar injury to the same foot in April.
"We're incredibly sorry for him," said Bayern's chief executive Karl-Heinz Rummenigge.
"The operation went perfectly, which is the most important thing for now. We and our captain are now looking to the future. Manuel will be back to his previous best and available to us again in January."
Bayern, Bundesliga champions for the past five seasons, have taken nine points from their first four games and face Schalke 04 away later on Tuesday.
(Writing by Brian Homewood in Geneva; Editing by Christian Radnedge)
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