The two Germany internationals have been punished for wearing incorrect kit during a training session at a winter camp in Qatar, according to newspaper Bild.
The pair are understood to have worn white socks instead of the black intended for use at the camp by the entire squad of the Bundesliga leaders.
"We have a common goal," head coach Jupp Heynckes was quoted as saying. "We need discipline. It starts with everyone wearing the same socks."
It is reported that club captain Philipp Lahm was instructed to determine the size of the fine and to collect the money from the pair.
Bayern chief Karl-Heinz Rummenigge backed Heynckes's decision, adding: "I like the way the coach acts."
The league leaders resume their domestic campaign at struggling Greuther Furth on Saturday January 19.