The boy, Siphokuhle Sikhakhane, 14, had gone to the shops with relatives on Saturday when they joined a crowd watching drag racers spinning cars at the local taxi rank.
Police said they had responded to the complaints of spinning cars and drag racing. When police arrived at the scene, a mob allegedly attacked the officers.
Gunshots were fired, and Sikhakhane was struck. He died on the scene.
Mchunu called for a full-scale probe into the matter.
“We are very disturbed at this unfortunate development where a young life was lost in the course of police doing their work. We wish to urge members of the community to refrain from attacking the police and allow them to do their work,” said Mchunu.
“We call on the police management in the province and Independent Police Investigative Directorate to conduct a full investigation into this matter.”
In a separate incident, an eight-year-old girl was shot dead allegedly by an angry neighbour in Mamelodi, in the northeast of Pretoria in January.
It is believed Nthabiseng Ramoroka was shot dead in Phomolong Extension by a neighbour, who was apparently fighting with his wife at the time of the incient.
The child, who had been sitting in the bedroom, was shot in the head after gunshots were fired.
The man believed to have fired the shots was later arrested.