The acting national police commissioner said at least 10 vehicles were burnt in Johannesburg and 14 in Durban.
The protests erupted over a Constitutional Court ruling easing access to asylum.
A new wave of xenophobic violence rocked South Africa on Thursday, with several cars razed and properties looted.
Like Nigeria, citizens of Algeria, Egypt, Libya, Sierra Leone, Somalia, South Sudan and Sudan are also ineligible for the broad visa-free scheme.
It warned, however, that growth remained too weak to generate sufficient productive employment and significantly reduce poverty.
“The nation is angry. The women of South Africa are angry, and their anger is justified. I too share that anger,” Mr Ramaphosa said.
Nigeria’s consulate general in Johannesburg has called for justice over the death of three nationals in separate incidents across South Africa.
Four innovators have been named finalists for the 2026 Africa Prize for Engineering Innovation for developing healthcare and agricultural technologies.
The Women for Change decried what it described as lack of urgent action from the government.
The RCCG Task Force welcomed the first batch of 100 Nigerians on Thursday night at the Murtala Muhammed International Airport, Lagos.
