Seven armed men apprehended security guards loading an ATM at Nyanga Junction around 9am, Lt-Col Andre Traut said.
The men ran to a getaway car with an undisclosed amount of money.
The group opened fire when they spotted a police patrol arriving on the scene.
Traut said police shot and wounded one of the men, in his thirties, in the pursuit. Another man, in his twenties, was arrested in NY3, Gugulethu.
The other five managed to flee with the cash.
Two firearms were recovered.
“It is fortunate that no one else was injured during the wild shoot-out staged by the suspects who displayed scant regard for the lives of others,” Traut said.