The fire broke out at around 2:15 on Friday morning in the small town of Ettenheim, police reported. Authorities have yet to offer an explanation of the cause.
The fire apparently started in a ward on the ground floor of the three-storey building. The body of the dead person was later found near this room.
The hospital was immediately evacuated - around 60 patients were moved into the city hall.
Fire fighters and Red Cross personnel subsequently helped to move five patients into other hospitals. Police said that the fire brigade managed to extinguish the fire relatively quickly.