Owen Green, 63, who was being treated for tuberculosis, was on oxygen when he succumbed to burn wounds on Sunday evening.
The cause of the fire, which started in ward G17, a general ward, at about 10pm, has yet to be determined.
Green’s niece, Geraldine Green, said when they were notified by police that her uncle had died, they thought it was due to his illness.
“My uncle was at Lentegeur Hospital at first and was recently moved to Groote Schuur Hospital.
"On Tuesday morning police came to our house in Eastridge, Mitchells Plain, to share the news of his passing.
“When they relayed the message, our family thought it was due to his illness.
"The police obviously couldn’t tell us how he had died and just asked us to go to the hospital. When we got to the hospital, we received the tragic news,” Geraldine said.
She said when they heard of how their uncle had died, “it was a huge shock and I could not stop crying”.
“Identifying his scorched body at the mortuary was an emotional experience.
"Just to think of how he had to suffer it’s not a nice feeling.
"We have been offered counselling by the hospital,” an emotional Geraldine said.
Groote Schuur Hospital spokesperson Alaric Jacobs said: “The hospital tried to get hold of the family but could not reach anyone on the telephone numbers available in the folder.
"The SAPS was therefore asked to locate the family at the address provided and they only managed to do this by Tuesday.”
Jacobs said the investigation to determine the cause of the fire is continuing.
Western Cape Provincial Health MEC Nomafrench Mbombo, who visited the hospital on Wednesday, said: “I would like to express my deepest condolences to the family of the patient.
"The matter is still under investigation, and we are working to establish the cause of the fire.
"I would like to commend our staff, who worked tirelessly alongside fire services to secure the safety of all other patients."