The France winger strained ligaments in his left ankle on Saturday during Bayern's 11th straight win - a 3-2 success against Fortuna Dusseldorf.
And a statement on the Bundesliga leaders' website confirmed Ribery will play no part at the Allianz Arena this week.
Bayern have a 3-1 advantage from the first leg, meaning Arsenal must score at least three times to deny their hosts a place in the quarter-finals.
No side has managed that this season against Jupp Heynckes' team, though the manager must also do without the suspended Jerome Boateng and Bastian Schweinsteiger.
And Arjen Robben, a natural replacement for Ribery, was missing at the weekend with a calf problem.