Ramokgopa said that the incidents had been confined, that no radioactive material was released into the environment, and that there was never any danger to nearby communities.
The incidents at the power plant, located about 30km north of Cape Town, occurred on June 30 and July 2 and 7.
According to the minister, the cause was a temporary power outage that disrupted the plant's ventilation systems.
He said the radiation doses received were lower than the exposure from a routine dental X-ray.
Velaphi Ntuli, head of the country's nuclear safety division, said the incidents did not meet the threshold for reportable nuclear safety events.
The government says nuclear energy will continue to play a key role in South Africa's future energy mix.
The country plans to add 5.2 gigawatts (GW) of nuclear generating capacity by 2039, despite public concerns over the expansion plans.
South Africa has struggled with severe electricity shortages and rolling blackouts in recent years.
The government views nuclear power as an important component of building a more reliable electricity supply.
South Africa's electricity generation remains heavily dependent on coal.
The government's long-term objective is to produce the majority of the country's electricity without fossil fuels by 2050.
