The cup holders have been drawn with the Bundesliga leaders in a repeat of last season's final, while third tier side Kickers Offenbach welcome Wolfsburg
BVB will have to defeat Die Roten on their home turf if they are to continue the defence of the cup when the competition resumes after the winter break.
Although an away tie at the Allianz Arena represents the most intimidating tie Jurgen Klopp's side could have been given, the Dortmund trainer has insisted his charges will relish the trip.
"My impression? My boys want to go to [the final in] Berlin," Klopp said when asked for his reaction by Sky.
Dortmund secured their passage to the last eight after thrashing Hannover 96 5-1.
"We have proven that we are in good form and we have earned the holidays now," added the 45-year-old.
The other quarter-finals will see Kickers Offenbach host VfL Wolfsburg, VfB Stuttgart entertain VfL Bochum, and SC Freiburg travel to FSV Mainz 05.
The matches are scheduled for February 26-27.