The attacking duo are believed to have come to blows during the Bavarians' victory over Los Blancos in the Champions League earlier this week and the club has taken measures
The France international is believed to have lashed out at his attacking colleague due to not being allowed to take a free kick in the 40th minute.
The mark on the Dutch winger's face was evident and the club has acted quickly to punish the perpetrator.
Despite Jupp Heynckes denying the incident had happened, the German newspaper indicate that Ribery has been given the sizable fine as punishment.
Bayern Munich faces Werder Bremen at the weekend before the return leg of its semifinal tie with Real Madrid next Wednesday.