President Cyril Ramaphosa said government will demonstrate its seriousness in terms of dealing with this matter.
The Witness reported that the 38-year-old married father of two said "the worst is over".
The patient and his wife were part of a group of 10 people who arrived back in South Africa from Italy on 1 March.
He told The Witness that his eight friends have also been isolated.
The man consulted a private general practitioner with a fever, headache, sore throat and a cough.
"The government will demonstrate its seriousness in terms of dealing with this matter," he told the media at an airforce base in the capital Pretoria.
"We are just at the beginning of this," he said, warning "it will turn out to be a national crisis".
Government is preparing to repatriate 184 of its citizens comprising students, teachers and other professionals working in China's Wuhan, the epicentre of the epidemic.
More than 90,000 people have been infected and over 3,000 killed worldwide since the virus first emerged in China in December.
- Additional reporting AFP