Of those injured, 11 of them are seriously hurt, while seven are fighting for their lives, a fire service spokesman said on Tuesday.
The cause of the fire which broke out in Marien Hospital in the Pempelfort district of the city is unclear. It had started on the second floor in the room of the patient who died.
From the room, the smoke spread over five floors of the hospital. Of the 72 people injured, 61 suffered smoke inhalation.
Some severely injured people were treated in the clinic's parking lot. A total of 19 people were taken to other hospitals, while one patient was flown by helicopter to a clinic in Aachen. The remaining patients were accommodated in other buildings of the hospital.
Firefighters needed around an hour to extinguish the blaze. It had become worse because oxygen from a pipe running through the room further intensified the fire.
In July, a patient died after a fire broke out in a pulmonary clinic in Cologne-Mehrheim. As a result, the German Foundation for Patient Protection had slammed the fire protection system in German clinics and nursing homes, calling it “insufficient”.