The attack occurred at a game farm around 270 kilometres (168 miles) northeast of the port city of Durban.
Police spokeswoman Nqobile Gwala said in a text message to AFP that a 25-year-old mother and her 16-month-old daughter were attacked around 1400 GMT at Kuleni Farm in the Hluhluwe area “when they were trampled by a giraffe”.
She said the girl was taken to a nearby doctor’s practice “where she died”, while the mother was rushed to hospital for medical attention where she is in a critical condition.
Police have launched an investigation into the incident. Giraffes do not usually attack humans.