Colonel Priscilla Naidu told News24 that David Oberholzer had apparently been confined to his room when the fire started at the Executive Frail Care Centre at about 08:00.
"He is an amputee. One of his legs was removed. He doesn't normally come down for breakfast at the centre's dining room. Every day, staff members usually take food up to him," said Naidu.
She said it has been believed that the elderly people living at the centre were having breakfast in their dining room at the time of the blaze.
"A worker at the centre was taking breakfast up to that person when she noticed smoke on the upper level. She ran back downstairs and alerted everyone," said Naidu.
She said everyone else at the centre had been evacuated.
"At this stage, the cause of the fire is yet to be determined. Police have opened an inquest docket," Naidu said.
It was not immediately clear whether Oberholzer had died of smoke inhalation or if he was burnt to death.
"The cause of death has not been determined but the post-mortem would determine that," Naidu said.
According to Atlas Security's Facebook page, the security company and the community of Morningside assisted in removing the residents to a nearby home.
Morningside Neighbourhood Watch's chairperson Charmaine Roos said: "A kind-hearted neighbour has opened her house completely to the affected elderly people who have been moved there, safe and sound with their carers."
Roos said they had been inundated with donations since the news of the fire got out.
"At this stage, it's very difficult to say what else the elderly people need. We've been inundated with food donations, clothes, towels, almost everything they need," she said.
Roos said those who still wanted to donate could call her on Monday.
"If anybody wants to make any further donation, they can rather give me a call on Monday. We will be able to give them a better idea on what else is needed once the elderly have been moved back to the centre," she said.
Roos' number is 0715625413.