The woman told the police that, during a heated argument, the man asked her if he was truly the baby's father.
"All she keeps asking is what happened to her baby"
As the man grew more and more angry, the woman took her newborn baby and fled the Johannesberg flat to a nearby petrol station.
But when the 32-year-old caught up with them, he ripped the child from the woman’s back, grabbed the baby girl by her feet, and smashed her against the woman.
He then dropped the baby onto the floor and continued his attack, until witnesses intervened.
According to police spokesman Warrant Officer Wanda Olivier, paramedics said the baby was lying on the ground wrapped in a towel and drowning in its own vomit when paramedics arrived at around 3am.
Emergency Services spokesman Xander Loubser said: “We took the baby to Kalafong Hospital where she later died of her injuries."
He added: "The mother had also sustained wounds to the head but we were not certain what caused them.”
Pastor Abraham Akih, who spoke on behalf of the family, said the mother had been left distraught.
“She is barely able to speak. All she keeps asking is what happened to her baby.
"Her two sisters and I are taking turns to watch her. But she is in a terrible state.”
The man will appear in Pretoria Magistrate’s Court on charges of murder.