Constable Thandile Gantsho, 38, died on Wednesday night from serious injuries, Colonel Tembinkosi Kinana said.
Last Wednesday, he and two other officers were searching homes for people wanted in connection with armed robberies in the area.
“Upon entering the dwelling the suspects opened fire at police officers. During a shootout with the robbers, one suspect was wounded and arrested and his 9mm firearm confiscated,” police said at the time.
Two officers, Constable Viwe Mpambane, 34, and Sergeant Mteteleli Damse, 39, were killed in the shootout.
The wounded suspect died in hospital the next day.
Western Cape police provincial commissioner Lt-Gen Arno Lamoer said the killing of police officers was an attack on the Constitution.
“We refuse to be side-tracked nor intimidated by cold-blooded criminals in our quest for the safety and security of our people.”