This is according to the latest modelling projections, says Health Minister Dr. Zweli Mkhize.
During a webinar on Tuesday, he says additional beds would now be added to the national count to help mitigate a projected shortfall.
The release of the modelling projections comes after mounting pressure for the government to share the data it was using to justify its decisions on the national lockdown and the regulations that have been put in place.
The Covid-19 Modelling Consortium, a group of scientists advising the government on projections and modelling which help to inform policy on dealing with the Coronavirus outbreak in the country, have presented two scenarios for the coming months.
Their modeling shows that by June, South Africa could see close to 500 Covid-19 deaths.
The number of those infected within the same period is expected to be just over 40 000.
As of last night, the country had recorded 17 200 cases and 312 deaths.
There have been 488 609 tests conducted, while recoveries stood at 7 960.
The projections painted an even grimmer picture for November, when infections are expected to be between 1 million and 1.5 million cases.
And just over 40 000 people could die from the virus by the same time.
Dr. Sheetal Silal of the Modelling and Simulation Hub, one of the organisations that have contributed to creating scientific models for Covid-19, stressed these models may be subject to change.
“These scenarios are founded on the assumption that after the five-week lockdown, Level 4 will continue for the next month, followed by a set of social distancing measures.
“It’s important to realise that these projections, as they are being updated on a regular basis, even these assumptions of what interventions may come into force in the coming months will also be updated,” Silal said.
The experts also looked at whether the two levels of the lockdown have helped so far.
The hard lockdown, or Level 5, lasted for five weeks, and this possibly helped reduce cases by between 40% and 60%.
Level 4 probably helped reduce cases by 25% and 35%.
Social distancing from the end of May could contribute to a reduction in cases between 10% and 20%.
Provinces were expected to see peaks in infections at different times, the experts said.
The projections also showed that South Africa could experience a severe shortage of hospital beds before the peak in cases is reached.
The country currently has over 125 000 beds available in the private and public sector.
Of these about 4 000 were ICU beds, but Silal said these may not be enough.