The incident occurred on Saturday afternoon when the victim, Sibongile Moima, was playing with her six-year-old friend at a private game reserve where her father, Piet Moima, is the foreman, state-run news agency Sapa reported.
Traumatised by the incident, the girl's grandfather, at whose house the shooting occurred, tried to commit suicide by hanging himself yesterday morning, it said.
The girl's grandfather had allegedly taken his revolver out of gun safe on Friday after robbers tried to break into his house.
The 60-year-old grandfather is due to appear in a court today, on charges relating to the negligent handling of a firearm, the agency quoted police spokeswoman, Colonel Ronel Otto, as saying.
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Otto said a murder charge was being investigated into the matter.
The children are thought to have found the gun in a wardrobe, in the grandparents' bedroom.
Despite efforts by the government to limit it, the level of private gun ownership remains high in South Africa, with some estimates putting the number of firearms at almost 6 or 12 for every 100 citizens, media reports said.