Mkhize and health officials from the World Health Organisation (WHO) and the National Institute for Communicable Diseases (NICD) addressed the media in Johannesburg on Friday morning.
At least 213 people have died in China and almost 10 000 cases of the virus have been reported.
The minister welcomed the WHO’s declaration of a global emergency.
Mkhize added that 55 international travellers were screened at points of entry into South Africa and were found to have a fever.
However, none of them tested positive for the coronavirus.
He also said that there was no evidence to support repatriation or emergency evacuations of South African citizens in China.
“We have remained vigilant on the development regarding the movement and behaviour of the viral infection across the world and we continue to engage with the international academic fraternity to better understand how this virus behaves,” Mkhize said.
The minister reiterated that South Africa was adequately prepared for active surveillance, early detection, isolation, case management, contact tracing and prevention of the infection.
“An emergency operations centre was activated on Thursday night and is currently operational,” Mkhize said.
“This means we have dedicated staff working exclusively on the coronavirus, monitoring and responding to all reports that they will proactively detect and follow up.”
Mkhize also said there were dedicated centres in all nine provinces for the isolation and treatment of suspected coronavirus cases.
All travellers will be screened at 36 points of entry into South Africa, Mkhize said.
“We are on high alert.”
Special measures have also been put in place at OR Tambo International Airport, which is the country’s busiest airport.
“Workers have commenced to develop a vaccine as soon as possible,” Mkhize said.
He added that South African citizens in China were “in safe hands”.
“We maintain that there is no evidence to support repatriation or emergency evacuations of SA citizens in China.”
Two South Africans in China have been placed in quarantine for 14 days as a precautionary measure, the minister said.
South African students who are studying in China, who are currently on holiday in South Africa, will not be returning to China just yet.
According to the WHO, common signs of infection include respiratory symptoms, fever, cough, shortness of breath and breathing difficulties. In more severe cases, infection can cause pneumonia, severe acute respiratory syndrome, kidney failure and even death.