Pro-Zuma protesters first took to the streets after the 79-year-old handed himself to authorities on Wednesday to begin a 15-month sentence.
But police now say criminals are taking advantage of the chaos which spread from his home province of KwaZulu-Natal to Johannesburg, in Gauteng and more than 60 people have so far been arrested.
The night before, some 300 people had barricaded a major highway in Johannesburg, according to the national intelligence body with Images showing buildings and cars on fire.
About 800 people were also involved in an incident in which one police officer was shot in Alexandra, a township in Johannesburg and two other officers were hurt.
Police also responded to reports of looting in both Johannesburg and KwaZulu-Natal.
 It is still unclear if they are linked to the pro-Zuma protests, however, KwaZulu-Natal police spokesman Jay Naicker told the press that officers had seen “criminals or opportunistic individuals trying to enrich themselves during this period”.
South Africa’s President Cyril Ramaphosa appealed for calm on Sunday evening, acknowledging that “there are those who may be hurt and angry”, but adding “there can never be any justification for such violent, destructive and disruptive actions”.
The jailing of a former president is unprecedented in South Africa which has been gripped by Zuma’s legal turmoil.
He was sentenced to 15 months in jail for contempt of court, after failing to attend an inquiry into corruption during his presidency.
Zuma denies corruption and has not co-operated with the legal process.
The case is due back in the Constitutional Court on Monday, with Zuma’s team hoping to get his sentence rescinded or reduced. On Friday, South Africa’s High Court dismissed an attempt to stay his arrest.