They were arrested along Stanford Road in the north of the city, Captain Johan Rheeder said.
The three, aged 21, 22, and 27, allegedly the instigators of the violence, were expected to appear in the Gelvandale Magistrate’s Court on Wednesday.
This brought the total number of arrests since Monday, when the violence began, to five. Residents have been protesting against a lack of teachers in local schools.
On Monday morning, a Daily Sun journalist was hit over the head and mugged. Later that day a News24 reporter was driving down Stanford Road when six children pelted his car with rocks and ran away.
On Tuesday, children pelted police cars with stones and put branches, burning tyres, rocks, and spikes on the road. Police retaliated with teargas and rubber bullets.
Principals of the affected schools were expected to meet provincial education department officials later on Tuesday to provide proof of teacher vacancies at their schools. This followed a decision taken at a meeting by a residents’ organisation, the Northern Areas Education Forum, on Monday night.
There would be a separate meeting between the forum and the provincial education MEC. The forum would report back to residents and a decision would be taken on the next steps to take.
The education department was expected to hold a media briefing later.
Resident Martin Hiles, 38, said he wanted local schools to improve.
"I don't want my child to grow up like I grew up. There are 60 kids in one class and there are no teachers. Kids don't go to school and then they become gangsters.
"I don't want my children to grow up and become gangsters. I want them to go to school and then go to university."