The former France international reportedly clashed with team-mate Mats Hummels on Tuesday and has suffered a strained thigh.
And the Bundesliga champions have confirmed a statement that Ribery is facing two weeks on the sidelines.
That means he is a serious doubt for the first leg of his side's Champions League last-16 tie against the Gunners, which takes place at the Allianz Arena on February 15.
It would not be the first time Ribery has missed games against Arsenal in recent years, with an ankle problem ruling him out of their meeting in 2013 before a buttock injury meant he was absent when the teams faced off again 12 months later.
There was more positive news for Bayern boss, Carlo Ancelotti, though, with Arturo Vidal and Arjen Robben both stepping up their recoveries from their own injury problems ahead of Saturday's Bundesliga match against Schalke.