The Bayern Munich CEO has hailed the France winger, with the winner of Uefa's Best Player in Europe award announced on Thursday ahead of the Super Cup final
Ribery opened the scoring for die Roten against Nurnberg on Saturday before Arjen Robben added another to complete a 2-0 win.
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"Franck has once again shown that he is extra class," the 57-year-old German was quoted by TZ.
"It would be nice if this was seen not only in Germany but also throughout Europe."
Ribery has been shortlisted alongside Lionel Messi and Cristiano Ronaldo for the Uefa Best Player in Europe award, and Rummenigge was keen to throw his weight behind his player's nomination before the winner is revealed on Thursday.
Ribery himself, who has scored 80 times in 240 games for the Bavarians, said little about his chances of taking the accolade.
"I've done everything individually and with the team," the former Olympique de Marseille man said.
"The goal I scored was extraordinary."
Bayern have made a perfect start to their Bundesliga defence having won all three of their opening fixtures.