At least 700 homes have been washed away near the capital, Pretoria, public broadcaster SABC reported.
The state-run power company warned of further electricity cuts, saying heavy rains had affected its operations.
The crisis has forced President Cyril Ramaphosa to shorten his trip to Egypt.
The power cuts, known as load shedding in South Africa, have halted gold and diamond production at some leading mines.
Harmony Gold said it had called off underground shifts.