At least 30 people have now died in the violence which has been engulfing parts of South Africa since the country's former President Jacob Zuma handed himself in to police last week.
Almost 800 people have been arrested in the unrest which began as protests following Zuma's jailing on Thursday.
But protests turned violent over the weekend, with fires set, highways blocked and businesses looted.
The military has now been deployed to help the overstretched police
Police Minister Bheki Cele told journalists on Tuesday that, if the looting continued, there was a risk areas could run out of basic food.
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 have accused some groups of taking advantage of the anger over Zuma's imprisonment to commit criminal acts, while others have said anger over unemployment and poverty are fuelling the chaos.
But Mr Cele warned that "no amount of unhappiness or personal circumstances from our people gives the right to anyone to loot, vandalise and do as they please and break the law".
He also revealed they were investigating 12 people for inciting violence.
There has been some concern over fake news online fuelling the unrest, while the governing African National Congress (ANC) had already revealed it was looking into tweets sent by Zuma's daughter, Duduzile Zuma-Sambudla.
"She will have to answer and explain what her tweets mean and where they're going to lead to," Jesse Duarte, the party's deputy secretary-general, said, according to South Africa's Daily Maverick.
Zuma was convicted of contempt of court last month 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 handed himself to police late on Wednesday.
He is hoping to get the sentence rescinded or reduced by the country's constitutional Court.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.
Analysis: What's behind the riots?
By Farouk Chothia, BBC News
The catalyst was the arrest last week of Zuma, with his supporters blockading major roads - the economic arteries of the nation - as they demanded the release of their political hero.
Low income levels and unemployment - standing at a record high of 32.6% among the workforce and even higher at 46.3% among young people - are seen as the ticking bombs that have exploded.
Many South Africans have been shaken by the riots that have swept through Zuma's political heartland of KwaZulu-Natal and the economic hub of Gauteng.
And many feel that his successor as president, Cyril Ramaphosa, has failed to provide decisive leadership - either to calm anger over Zuma's imprisonment or to reassure South Africans that they will be safe.
Mr Ramaphosa was accused of belatedly deploying troops - and only 2,500 of them compared with the 70,000 he deployed to enforce a nationwide lockdown to curb the spread of Covid-19 last year.
But there is no agreement over the deployment - the Economic Freedom Fighters opposition party has opposed it, saying the solution lay in "political intervention and engagement with our people".
Many residents in affected areas have remained at home, and some have formed what local media call "defence squads" to protect their neighbourhoods and businesses as looting continues.
There is no doubt that the unrest is the biggest security challenge that Mr Ramaphosa has faced since he became president in 2019, and it is bound to worsen the economic crisis, already hit by the Covid pandemic, as many businesses, including supermarkets, pharmacies and other retail stores, have been destroyed.
Video footage shows that even a blood bank was looted in the coastal city of Durban, as Mr Ramaphosa addressed the nation on Monday night.
Source: BBC News