Neuer has just led Bayern to a tenth straight Bundesliga title and will be 38 by the time his new deal expires.
“Manuel Neuer is the best goalkeeper in the world and has been setting standards at international level for years,” said Bayern CEO Oliver Kahn.
“It is a tremendous achievement to be able to deliver world-class performances so consistently over such a long period of time.
“Manuel is one of the defining figures in the history of FC Bayern.”
Neuer, a 2014 World Cup winner, left Schalke in 2011 to join Bayern, winning Champions League titles in 2013 and 2020 and has made 472 appearances for them.
Neuer is the second long-serving veteran to have signed a year’s extension for Bayern recently after Thomas Mueller.
However, the future of Bayern forwards Robert Lewandowski and Serge Gnabry, whose current contracts both expire in 2023, remains unclear.