Four men aged between 40 and 50 were arrested on Sunday. A police spokesman said there was evidence they were planning terror acts around the country and not just at the ANC meeting in the central city of Bloemfontein.
Most of South Africa's whites accepted the ANC's victory in the 1994 election that brought Nelson Mandela to power and ended decades of white-minority rule. However, a handful continues to oppose the historic settlement.
"Their acts are widespread. We arrested them in different provinces," the spokesman said.
An ANC spokesman said preliminary information suggested the men were planning to bomb the marquee where Mr Zuma and 4500 delegates are holding a five-day meeting to choose the ANC's leadership for the next five years. "This would have been an act of terrorism that South Africa can ill afford," he said.
The Federal Freedom Party, a fringe group fighting for self-determination for the white Afrikaner minority, confirmed two of those arrested were FFP members but denied any role in the plot.