Local authorities are calling for a state of disaster to be declared, after some areas saw months worth of rain fall in one day.
Officials have called it “one of the worst weather storms in the history of our country”.
President Cyril Ramaphosa has visited the area and pledged to help.
“Even though your hearts are in pain, we’re here for you,” the Reuters news agency quotes him as saying.
Photos from the area’s main city, Durban, show wrecked homes and cars submerged in water.
Months worth of rain fell in a single day in some areas, and mudslides have brought traffic to a standstill. Some motorways are so submerged that only the tops of traffic lights can be seen, according to the AFP news agency.
Many are people are still missing.
Ron Naidoo, a community pastor in the town of Tongaat, told the BBC he had been kept awake through the night by the rising floodwaters and had seen police drag a car out of the river with a body inside.
“It was traumatic because it is the first time that we have seen the river rise so high here,” he continued.
The KwaZulu-Natal provincial government estimates that billions of rand worth of damage has been caused to properties and infrastructure, describing the heavy rains as unleashing “untold havoc” in a statement on Facebook.
Electricity and water treatment plants have been “flooded out”, Durban’s Mayor Mxolisi Kaunda told the BBC.
Durban port – the busiest in South Africa – has also been affected. Terminals cannot be accessed because of damage to the roads, and operations at the port have now been suspended, state-owned logistics company Transnet said.
Parts of the crucial N3 highway which connects Durban to the economic heartland of Gauteng province have been blocked.
Communications have also been disrupted with two major networks reporting that more than 900 of their cell phone towers are down.
Declaring the flood-stricken area a disaster zone will “enable the province to apply for emergency funding” from the National Treasury and assist with necessary reconstruction work, authorities say.
There are also reports of looting in Durban, which the local government has condemned: “We will not allow what is a tragic development in our province to be taken advantage of,” it said.
The government is calling on people to stay safe by avoiding flooded roads and bridges and to evacuate to higher ground if they live in low-lying areas.
The stormy weather comes as scientists warned that climate change is fuelling heavier rainfall than usual in southern Africa.
At the start of the year, the region was hit by three cyclones and two tropical storms in six weeks, which primarily affected Madagascar, Mozambique and Malawi and inflicted widescale damage with 230 reported deaths according to the World Weather Attribution (WWA).