Baby Ashleigh Louw died on Friday, Chris Hani Baragwanath Hospital clinical manager Dr Pungie Lingham said.
"Sadly, she has passed on," he said. "Our condolences go out to the family."
He said she died around midday but could not reveal the cause of death for privacy reasons.
"Baby Ashleigh was very ill and she's been in ICU [intensive care unit] under very intense management both medically and otherwise," said Lingham.
Born on January 9, Ashleigh was operated on January 17 after being born with her heart outside her chest, covered only by a thin layer of skin.
The condition is known as Pentallogy of Cantrell which occurs in one in a million babies.
Minister sends condolences
Health Minister Aaron Motsoaledi sent his condolences to the family of Ashleigh.
"Our prayers are with them during these difficult times. The loss of such a young life is painful to all of us," said Motsoaledi in a statement. He praised the medical team at the hospital for their work and contribution to "medical history".
"I wish to pay tribute to the team that worked hard in trying to save the little life that we have just lost. I am aware that they were dealing with a very complicated and rare condition and there is no doubt that they have made medical history in our country," said Motsoaledi.
"We are always encouraged by the dedication of our healthcare workers to do their utmost even under the trying circumstances such as those faced by our hospitals. We are very proud of them.". - (Sapa, March 2010)