The country closed its borders in March to limit the spread of the virus.
It will from Thursday reopen some land borders and its three main airports in Cape Town, Durban and Johannesburg.
The Foreign Minister, Naledi Pandor, said all arriving travellers must produce a Covid-19 testing certificate from their countries and will be screened on arrival.
"Only citizens who are investors, diplomats, high-skills visa holders and businesspeople [coming from the high-risk countries] will be allowed, Ms Pandor told journalists on Wednesday.
South Africa has been the worse hit country by the pandemic in Africa. It has so far confirmed 674,000 cases, about half the number reported in Africa.