At least eight people were killed as winds reached around 100 kilometres per hour and heavy rain and huge waves battered much of the Western Cape, including Cape Town, where the fatalities all occurred.
According to the newspaper, people in the Whale Rock and Longships areas, near Robberg, were being evacuated.
The severe weather, dubbed "the cape storm" and thought to be one of the worst for 30 years, has left dozens of people in shantytowns around Cape Town homeless - as well as forcing schools and universities to close.
Eleanore Bouw-Spies, Knysna's mayor, described the fires as the worst in decades.
Local media reported Thursday that the military planned to help emergency responders in Knysna, which lies on the Garden Route, a popular tourist destination on the southern coast of South Africa.
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Cape Town workers said they had taken measures to protect some poor residents, who live in sprawling neighborhoods of makeshift homes.
The weather also caused chaos throughout the city, knocking out electricity and cancelling flights and rail services.
Four people died in a fire caused by a lightning strike in the northern Cape Town suburb of Kraaifontein, while another was killed in the Lavender Hill area when a building collapsed, according to the provincial government.
While Cape Town badly needs rain following the worst drought on record, the downpour will only marginally alleviate water shortages, city authorities said.
The BBC reports from Cape Town that before the storm, there had been several interfaith meetings to pray for rain.