Foul play has been ruled out in the shootings of a police captain and her two sons at their home in Centurion, Pretoria police said on Sunday.

Captain Annake van Niekerk gunned down her three-month-old baby, shot her 12-year-old son in the head and then turned the gun on herself on Saturday afternoon, Inspector Wanda Olivier said.

"We can confirm that there was no foul play... everything shows the mother used the firearm. Forensic testing shows she did fire the gun... they did [gunpowder] residue tests and residue was found on her hands."

Van Niekerk's 12-year-old son died at the Unitas hospital on Saturday afternoon shortly after her ex-husband stumbled on the scene around noon.

The motive for the murders was not yet known.

A captain at the Pretoria criminal records division, she lived alone with her two children.

"Investigations are continuing," Olivier said.