Neuer, who was arrived from Schalke 04 in 2011, will become the fourth goalkeeper to captain Bayern — following in the footsteps of Oliver Kahn, Raimond Aumann and Sepp Maier.
The 31-year-old also skippers the German national team, after taking over from Bastian Schweinsteiger last year.
“Our No. 1 one is the No. 1,” Rummenigge said in Shanghai.
“Manuel is a seasoned professional and will take over the armband from Philipp.”
Neuer did not travel for the summer tour to Asia, opting to remain in Munich to work on his comeback from injury. He is expected to be available for their opening Bundesliga game against Leverkusen on August 18.