Police said disturbances had intensified and 219 people were arrested as the controversial ex-leader challenged his 15-month prison term in the country's top court.
Smoke from burning buildings swirled in the air as items from burgled shops lay strewn by the side of the road in Pietermaritzburg in Zuma's home province of KwaZulu-Natal (KZN).
The sporadic pro-Zuma protests that broke out when he handed himself over last week have quickly escalated into looting and arson, mainly in KZN but also in Gauteng where the biggest city Johannesburg is.
Some Covid-19 vaccination sites and clinics in Gauteng and KZN were shuttered due to safety concerns, the Gauteng provincial government and an independent pharmacy association said, further delaying a sluggish immunisation campaign.
Opportunistic criminals appear to be taking advantage of the anger some feel over Zuma's incarceration to steal and cause destruction, police said.
A statement from the military said "pre-deployment processes had started" following a request for assistance from a government intelligence body, but a Reuters cameraman in Pietermaritzburg saw armed soldiers already in the streets.
President Cyril Ramaphosa would address the nation about the violence, his office said.
Any confrontation with soldiers risks fuelling claims by Zuma and his supporters that they are victims of a politically-motivated crackdown by his successor Ramaphosa.
Zuma, 79, was sentenced late last month for defying a constitutional court order to give evidence at an inquiry investigating high-level corruption during his nine years in office until 2018.
The decision to jail him resulted from legal proceedings seen as a test of post-apartheid South Africa's ability to enforce the rule of law, including against powerful politicians.
In a virtual hearing on Monday, Zuma's counsel asked the constitutional court to rescind his jail term, citing a rule that judgments can be reconsidered if made in the absence of the affected person or containing a patent error. But legal experts say Zuma's chances of success are slim.
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Footage shot by Reuters in the Katlehong township in Gauteng showed police firing rubber bullets at looters to disperse them.
At the Jabulani Mall in Soweto, looters brazenly walked past TV cameras carrying armfuls of stolen goods.
Liquor stores were among those affected, as the sale of alcohol is currently banned under Covid-19 restrictions designed to ease pressure on hospitals, as were shops of companies like pharmacy group Clicks, and food retailers Pick n Pay and Shoprite.
As of Monday morning the bodies of four people had been found — at least two with gunshot wounds — in Gauteng, intelligence structure NatJOINTS said. Two deaths had happened in KZN, and all six were being investigated.
Ramaphosa said on Sunday there was no justification for violence and that it was damaging efforts to rebuild the economy after Covid-19.
The governing African National Congress (ANC) said on Monday that the poor would bear the brunt of the destruction as critical public services had been disrupted and several small businesses destroyed.
Zuma's imprisonment marks a significant fall from stature for a leading figure in the ANC.
He was once jailed by South Africa's pre-1994 white-minority rulers for his efforts to make all citizens equal before the law, but for many his reputation is now tarnished after a string of sleaze and graft scandals.
The corruption inquiry that Zuma has refused to cooperate with is examining allegations that he allowed three Indian-born businessmen, Atul, Ajay and Rajesh Gupta, to plunder state resources and peddle influence over government policy. He and the Gupta brothers, who fled the country after his ouster, deny wrongdoing.
Zuma also faces a corruption case relating to a $2 billion arms deal in 1999 when he was deputy president. He denies the charges in that case.