Seven people from the group of 10 people who returned from Italy have now tested positive for COVID-19 in South Africa.
A senior epidemiologist from the National Institute for Communicable Diseases, Sibongile Walaza, said all seven have presented with mild symptoms of the illness.
Walaza said the aim is to reduce the rate and number of infections while preparing for the possibility of community infection.
She encouraged people should get vaccines for influenza in order to distinguish between infections of flu and COVID-19 as the novel coronavirus presents with flu-like symptoms.
Walaza said people should be cautious, stay away from work if they are feeling ill, keep sick children away from school, and maintain personal hygiene.