At least 30 people have been killed and nearly 800 arrested, shops rooted and buildings set on fire since Zuma handed himself in to police last week.
Troops have been deployed in Gauteng province, and in Zuma’s home province of KwaZulu-Natal.
Zuma was convicted of contempt of court after failing to attend an inquiry into corruption during his presidency.
The 79-year-old, who denies corruption, was given a 15-month prison sentence. He is hoping to get the sentence rescinded or reduced by the country’s constitutional Court. However, legal experts say his chances of success are slim.
Police Minister Bheki Cele told journalists on Tuesday that if the looting continued, there was a risk areas could run out of basic goods.
However, Defence Minister Nosiviwe Mapisa-Nqakula said there was not yet a need to declare a state of emergency over the violence in KwaZulu-Natal and Gauteng provinces.
KwaZulu-Natal Premier Sihle Zikalala said some 26 people had been killed in the province so far, including a 15-year-old boy, EWN reports. Six deaths have been confirmed in Gauteng, news agency AFP says.
Officials accuse people for taking advantage of Zuma’s imprisonment to commit crimes where as others say unemployment and poverty are fueling the chaos among people rioting in South Africa
In a televised address on Monday, Mr Ramaphosa condemned “acts of public violence of a kind rarely seen in the history of our democracy”.
Images from Durban, in KwaZulu-Natal, showed shops ransacked and businesses set on fire. In Johannesburg looters were seen taking televisions, microwave ovens and clothes.
“What we are witnessing now are opportunistic acts of criminality, with groups of people instigating chaos merely as a cover for looting and theft,” Mr Ramaphosa said.
“There is no grievance or political cause that can justify the violence and destruction that we have seen in parts of KwaZulu-Natal and Gauteng.”
On Sunday, protesters armed with sticks, golf clubs and branches were seen marching through Johannesburg’s central business district.