Jurgen Klopp's side memorably secured a 5-2 win in last season's showpiece to complete a league and cup double.
Dortmund's hopes of repeating the feat have been undermined by falling 12 points behind Bayern in the Bundesliga this term and they must now travel to Munich in the last eight of the DFB-Pokal.
"We accept it, even though we would have preferred a home game," Dortmund chief executive officer Hans-Joachim Watzke told the DFB's official website.
Elsewhere, there was one other all-Bundesliga tie with Mainz to face Freiburg.
Third division Kickers Offenbach will be at home to Wolfsburg while Stuttgart host second-tier Bochum.
The ties are due to be played on February 26-27.