Europol revealed that 380 matches and 425 match officials, players, club officials and criminals were involved in the scandal.
Rummenigge blasted those involved and said that fans coming to the matches must watch a fair and "reputable" game.
"It is about the credibility of football," Bayern's official website quotes him as saying. "[Those found guilty] should suffer a severe punishment.
"When people go to the stadium, they need to know that everything there is clean and reputable before him."
The investigation lasted 18 months.