"It's a broken rib, he probably won't play again this year," said coach Vincent Kompany ahead of Bayern's Champions League game against Shakhtar Donetsk in Gelsenkirchen on Tuesday.
"It's important that it heals, then we'll have Manu back in January."
Neuer suffered the injury in the cup defeat to Bayer Leverkusen - during a foul on Jeremie Frimpong for which he received the first red card of his career.
Kompany confirmed on Monday that, as in the Bavarian's 4-2 win against Heidenheim, Neuer will be replaced by understudy Daniel Peretz.
Midfielder Konrad Laimer has "full confidence" in the Israel international, who will be making his debut in the competition.
The 24-year-old had already deputised for Neuer in the cup and in the Bundesliga and "he did a very good job", according to the Austrian
"We want to make it as easy as possible for him." Kompany also emphasised.
"He deserves it, he should just be himself."
Neuer is just one of numerous injured players Kompany will have to do without. "There are a lot of players out at the moment," said the Belgian coach.
"But we believe that we'll have a big squad again at the start of January. We've actually come through quite well."
In addition to Neuer, other players who will miss the match against the Ukrainian champions include star striker Harry Kane, Kingsley Coman, Alphonso Davies, Joao Palhinha and Serge Gnabry.
Bayern still have Bundesliga matches at Mainz 05 and against RB Leipzig on the programme before the German winter break.