Ribery, 35, was reportedly involved in an altercation with a television reporter on Saturday evening after the 3-2 defeat to their undefeated title rivals.
Bild reported that he was angered by the analysis of compatriot Patrick Guillou following Bayern's dramatic defeat to Lucien Favre's side and lashed out at him before storming out.
The newspaper cites witnesses who claim that Ribery struck Guillou on three occasions as he left Signal Iduna Park after the veteran was questioned over two individual errors that led to his side conceding.
Bayern sporting director Hasan Salihamidzic confirmed to the German publication that he was aware of the incident and has already spoken to Guillou - who works for beIN Sports - in a bid to clear the air.
"Franck Ribery has informed us that he had a dispute with his compatriot Patrick Guillou, whom he knows well for many years," he said.
"We agreed with Patrick Guillou on Saturday night that we would promptly speak at a face-to-face meeting about how to get the matter out of the way. Mr. Guillou has already signalled that this is in his interest."
Ribery has yet to open his account under manager Niko Kovac this season, after 15 games across all competitions.