Jurgen Klopp's side signed defender Manuel Friedrich on Wednesday, with Marcel Schmelzer, Mats Hummels, Lukas Piszczek and Neven Subotic all on the sidelines
Right-back Lukasz Piszczek has missed the whole campaign with a groin injury, while Neven Subotic was ruled out for six months after tearing cruciate knee ligaments in the 2-1 defeat to Wolfsburg before the international break.
Dortmund coach Jurgen Klopp has seen his options at the back further depleted this week, with the news that centre-back Mats Hummels will be absent until January with a broken foot, while left-back Marcel Schmelzer faces a month out with a torn calf muscle.
To alleviate this defensive crisis, the BVB boss has drafted in free agent Manuel Friedrich, who had been unattached since leaving Bayer Leverkusen in the close-season.
Dortmund will be looking for a strong response to two defeats in the space of four days before the international break.
Klopp's side first fell to a 1-0 home loss to Arsenal in the Champions League that has left their participation in Europe's premier competition in the balance, while the Wolfsburg defeat saw them drop four points adrift of Bayern.
Bayern coach Pep Guardiola has injury trouble of his own, though, with France international Franck Ribery ruled out with a fractured rib.
The Ballon d'Or contender joins Bastian Schweinsteiger (ankle), Claudio Pizarro (thigh), Xherdan Shaqiri (thigh) and Holger Badstuber (knee) on the sidelines.
Reigning champions Bayern are in superb form ahead of the crunch fixture, though, and are looking to extend their record 37-match unbeaten run in Germany's top flight.