Cologne's Rasmus Carstensen, left, tries to score as Bayern's goalkeeper Manuel Neuer saves during the German Bundesliga soccer match between FC Cologne and Bayern Munich in Cologne, Germany, Friday, Nov. 24, 2023. Photo: AP
Neuer, 37, originally joined the Bavarians in 2011 before being named captain six years later.
He returned from 10 months out with a knee injury in October.
"I'm happy to be staying at FC Bayern for another year," Neuer said in a club statement.
"After my long injury, I'm back in full swing.
"It's immense fun for me to be on the pitch with this team," he added.
Neuer has won the Champions League twice and the Bundesliga on 11 occasions with Bayern as well as the 2014 World Cup for Germany.
The keeper's number two Sven Ulreich has also agreed a new deal, aged 35.
Second-placed Bayern trail league leaders Bayer Leverkusen by two points before hosting lowly Union Berlin on Saturday.
In the Champions League, they have already qualified for the last 16 with two group games remaining including Wednesday's home game with Copenhagen.
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