The pair are reported to have had a heated debate in the dressing room after discussing who should take a free-kick late in the first half in Tuesday night's 2-1 win over Real Madrid in the Champions League.
Sport Bild magazine claims Ribery punched Robben in the face and pictures appeared after the game of Robben with a cut under his right eye.
On Saturday, the Bild newspaper claims Ribery has been fined 50,000 euros for the incident while the pair rarely exchanged glances, let alone passes, in Friday's final training session ahead of the trip to Werder Bremen.
Coach Jupp Heynckes was diplomatic when pressed on the matter at Friday's pre-match press conference, neither confirming nor denying the incident.
"There are taboo zones within a football team," he is quoted as saying by the Bild.
"Given the huge media presence, that is also necessary. I believe that internal matters must remain internal, whether that is here at our training ground or in the dressing room.
"Everything else is speculation and I will not respond to that."
Both Ribery and Robben are set to occupy the bench on Saturday as Heynckes rests his key players in view of the trip to Madrid next Wednesday.