The 30-year-old suffered a minor fracture in France's 3-0 win over Ukraine on Tuesday as he helped les Bleus turn around a 2-0 loss from the first leg of their qualification playoff in order to seal a ticket for the 2014 World Cup.
Tuesday's win came at a cost, though, as Ribery will now miss the highly-anticipated game against second-placed Dortmund, which he admits is deeply frustrating.
"This is very bitter. I really wanted to take part in the big game against Dortmund," Ribery told the official Bayern website.
"However, I am confident that the team will be successful without me as well this time."
Bayern will also be without the injured Bastian Schweinsteiger, Claudio Pizarro, Xherdan Shaqiri and Holger Badstuber on Saturday, although Jerome Boateng has confirmed he will be fit to play a part.