The man shouted "Seig Heil" during a period of silence for long-standing HSV physio Hermann Rieger, who passed away last week.
He has been promptly punished, having been hit with three-year nationwide stadium ban in addition to an exile from Signal Iduna Park until June 2020 from Dortmund.
"Borussia Dortmund have imposed a stadium ban until June 30, 2020 on a man who disturbed the minute's silence for HSV legend Hermann Rieger with a right-wing interjection," a club statement read.
"Borussia Dortmund thank Hamburg for their good cooperation. Borussia Dortmund believe deeply in tolerance and diversity and will fight with every means against racism and discrimination."
Dortmund, which lost the game at the Imtech Arena 3-0, takes on Zenit St Petersburg in the Champions League on Tuesday.