The National Institute of Communicable Diseases (NICD) confirmed on Monday that the total number of confirmed cases have risen to 62.
Of the new confirmed cases, was the first for Limpopo.
Health Minister Zweli Mkhize also confirmed that local transmissions were under investigation but further details would be announced at a later stage.
In his announcement to the nation on Sunday, President Cyril Ramaphosa said there had been local transmissions of the coronavirus (Covid-19 virus). Now, according to the Minister of Health, Zweli Mkhize, this is under investigation, with one of the suspected cases a three-year-old child in KwaZulu-Natal.
"We will confirm it as soon as we have more information.
"One of the cases is a three-year-old child, who is linked to a contact. But we're trying to establish the exact connection between them," Mkhize said.
He added that he would not go into detail, but said, at this stage, the child's parents were healthy.
Social Development Minister Lindiwe Zulu says government will be monitoring South African citizens outside the country, including those still in Wuhan who were not able to board the plane.
Speaking at an inter-ministerial briefing on Monday, a day after President Cyril Ramaphosa’s declaration of a state of disaster in light of the coronavirus outbreak, Zulu said government was in contact with the remaining South Africans in Wuhan, as well as their families.
Last week, South Africans in Wuhan, China – the initial epicentre of the outbreak – were repatriated.
"There are four particular cases of those who could not board the plane. I can imagine the pain, having been left behind.
"But we are in contact with them, they are in a good space and we have been in contact with the families of the four."
Play your part, Motshekga tells parents as schools shut over Covid-19 virus.
In his address to the nation on Sunday, President Cyril Ramaphosa announced that schools would be closed from Wednesday, which is why the government has urged parents to take responsibility for their children in the fight against the spread of the coronavirus.
Basic Education Minister Angie Motshekga and Social Development Minister Lindiwe Zulu called on parents and communities to play their part in navigating the pandemic.
"Parents must step up and work with social development, work with government," said Motshekga.
She responded to criticism of schools closing early, saying it was only a few days as the end of the term was a week away.
"Communities will be taking care of their children as they always do. We close for three weeks in June and they know how to look after their children as they always do… In December, we close for six weeks," she pointed out.
While panic grips the country following President Cyril Ramaphosa's declaration that the coronavirus outbreak is a national disaster, the Gauteng health department says that it will not be conducting mass screenings at this stage.
This comes after members of the public flocked to Charlotte Maxeke Johannesburg Academic Hospital to have themselves screened for the deadly virus which first emerged in Wuhan, China. There were 62 confirmed cases in South Africa at the time of publication.
A 33-year-old who wanted to remain anonymous, told News24 on Monday that she was "turned away" when she approached the hospital on Monday to be tested after she experienced some symptoms.
"I am experiencing a fever, my lungs are sore and I have a sore throat. So I went in and the doctor said she cannot do the test on me because I did not have direct contact with any of the confirmed cases," she told News24.
WHAT'S HAPPENING IN THE REST OF THE WORLD
For the latest global data, follow this interactive map from Johns Hopkins University & Medicine.
Positive cases worldwide are now close to 180 000, while deaths are now more than 7 000.
The spread in Italy has been dramatic, with now nearly 30 000 cases, and more than 2 000 deaths.
Iran has just short of 15 000 cases, with nearly 900 deaths,
US nightlife capitals New York and Los Angeles ordered bars and restaurants to close or go take-out only as the country scrambled to contain the coronavirus pandemic and the Federal Reserve slashed rates to stem the fallout.
The fast-spreading outbreak has claimed almost 70 lives in the United States, disrupting every walk of life as Americans – watching Europe plunge into lockdown, and panic-buying at home – brace for what is to come.
Faced with an economic shutdown, the Fed announced a raft of emergency measures to shore up confidence and keep the financial sector running, including cutting the key interest rate to 0-0.25%.
President Donald Trump, addressing a now-daily briefing of the White House task force on the crisis, praised the "phenomenal" action by the Fed, and sought a reassuring tone even as he pleaded with Americans to stop stripping store shelves bare.
The coronavirus outbreak in France is "very worrying" and "deteriorating very fast", the head of the country's health service said on Monday.
"The number of cases double every three days," Jerome Salomon said on France Inter.
"I want our citizens to realise that there are people who are sick, who are in intensive care and that (their number) runs into hundreds," he said.
READ MORE | France says coronavirus situation 'deteriorating very fast'
As the new coronavirus rapidly spreads around the world, scientists are still trying to figure out how exactly this virus will affect us.
A hot topic is whether climate and weather play a part in the spreading of the disease.
Surely it’s simply too hot in South Africa right now, and surely we can contain an outbreak before winter hits us?
Will the pandemic start flat-lining in the Northern Hemisphere as their spring arrives?
HEALTH TIPS (as recommended by the NICD and WHO)
• Avoid contact with people who have respiratory infections
• Maintain social distancing – stay at least one metre away from somebody who is coughing or sneezing
• Practise frequent hand-washing, especially after direct contact with ill people or their environment
• Avoid touching your eyes, nose and mouth, as your hands touch many surfaces and could potentially transfer the virus
• Practise respiratory hygiene – cover your mouth with your bent elbow or tissue when you cough or sneeze. Remember to dispose the tissue immediately after use.
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