Rummenigge also said Kahn had been devastated by the decision of Germany coach Juergen Klinsmann to relegate him to second put him on the bench behind Arsenal's Jens Lehmann.
"We were really worried about him. He was just floored. But he reacted well. He's going to quit the national team after the World Cup and concentrate on Bayern Munich," Rummenigge said in an interview with Bild newspaper.
Kahn captained Germany to the final of the last World Cup in South Korea and Japan, and was named player of the 2002 tournament.
One of Klinsmann's first acts as coach after taking over in 2004 was to strip Kahn of the captaincy and tell him that he faced a battle with Lehmann for the number one spot.
Since then the two keeper's were rotated, although a mistake by Kahn in the 4-1 victory over the U.S. in March seemed to have made up Klinsmann's mind on his first choice.
Rummenigge also criticised Michael Ballack, who has kept the club in the dark about his future plans, and Chelsea's Russian owner Roman Abramovic. The midfielder is expected to join English champions Chelsea for next season.
"But what we find fault with is the way he has messed us about (with his contract). Everyone knows he is going to Chelsea. But he has stayed secretive and it's partly his own fault that fans are jeering him."
"We're only a small wheel, an underdog. We cannot keep up with Real Madrid, Barcelona or Abramovic, who is damaging football. We have to show humility in the Champions League from now on."