The France international has been one of the Roten's undisputed star players this term, and the chairman has acknowledged he is a key figure
The Bavarians had to make do without the services of the Frenchman in the Bundesliga match against Nurnberg at the weekend due to a rib injury, resulting in them having to settle for a draw in his absence.
And the Bayern Munich chairman concedes his side are reliant on Ribery's quality.
"Our game depends a lot on Ribery. Like [Lionel] Messi at Barcelona, [Cristiano] Ronaldo at Real Madrid, or [Wayne] Rooney at Manchester United," Rummenigge was quoted as saying by Bild.
"That's simply the way it is. Every big team has some key players, on whom they tend to rely."
The winger is doubtful for Tuesday's Champions League match against Valencia, but Bayern are hopeful that the 29-year-old will be fit enough to feature from the start.
Ribery has made 13 appearances in all competitions for Bayern this season, netting four goals in the process.