Dortmund beat Eintracht Frankfurt 2-1 in May's Berlin final under Thomas Tuchel and his successor Peter Bosz has now learned of his first cup opponents.
Rielasingen-Arlen qualified for the tournament with victory in last season's South Baden Cup and have been rewarded with a visit from giants Dortmund.
Bundesliga champions Bayern, meanwhile, travel to Chemnitzer of the third tier, having lost to Dortmund in a thrilling semi-final last term.
Chemnitzer were Saxony Cup victors, while fellow Verbandspokal winners Sportfreunde Dorfmerkingen host RB Leipzig.
Borussia Dortmund will face 1. FC Rielasingen-Arlen in the first round of the German Cup. pic.twitter.com/scc8roz6c2— Borussia Dortmund (@BVB) June 11, 2017