The country has Africa's only nuclear power station but the Koeberg plant near Cape Town is currently only working at half capacity.
The first of the new units will probably come on stream in 2032 or 2033, Zizamele Mbambo, the energy ministry's deputy director general of nuclear power, told a press briefing.
He said South Africa had already asked "different vendors" for proposals.
Electricity Minister Kgosientsho Ramokgopa said the extra 2,500MW of extra nuclear power would be "a significant milestone".
He added that it would be part of the government action to "ending the existential challenge that is confronting the country" over power shortages and long term energy security.
Rotating power cuts of up to 12 hours a day over the past 15 years have badly hit the economy and the government's reputation as it heads into an election next year.
National power company Eskom has been tainted by corruption and maintenance problems that have led to the power cuts.
In a bid to extend the life of the Koeberg plant by 20 years, one unit was closed for nearly a year and the second unit was shut down for maintenance this week.
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