An argument is said to have taken place during Bayern's 2-1 victory at home to Real Madrid in the teams' Champions League semi-final first leg on Tuesday, with Robben apparently instructing Ribery to let Toni Kroos take a free-kick in first-half injury time.
The row then reportedly escalated, with Sport Bild claiming Ribery and Robben became involved in a verbal row at half-time before the former aimed a punch at the latter. Robben afterwards appeared to have bruising under his eye.
Media director Markus Horwick said: "Whatever happens in the dressing room stays in the dressing room. We will not be adding any further comment."
Sport Bild reports that a clear-the-air meeting was held on Wednesday. Ribery is said to have apologised and accepted a fine for his actions.