The blaze broke out overnight in a ground-floor unit of the shelter located in a former US army barracks in the southern city of Bamberg, police said.
"Emergency services discovered a lifeless body in the apartment," said a police spokesman, without providing any personal details about the victim.
Another 15 residents suffered smoke inhalation, and seven of these had to be taken to hospital for treatment.
Police said initial indications were that the fire broke out inside the victim's room, and that the investigation into the cause of the blaze was continuing.
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