He said in one incident a family of four died in a fire caused by lightning, while another person died due to a building collapse.
"We appeal to the public to remain indoors if possible and to steer clear of coastal areas as the frontal system is coinciding with a spring tide, resulting in massive swells", the City of Cape Town said.
The storm, which has not yet reached its peak, hit parts of the Cape Peninsula on Tuesday night destroying homes and breaking trees.
He added that many people had been injured by flying debris.
The storm comes at the end of the region's worst drought in a century.
Around 700 structures have been affected by flooding, according to the City of Cape Town's Disaster Management. Now it urges residents to capture rain from the storm in containers for flushing toilets and other needs.
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"The South African Weather Services has advised that the current weather conditions will persist until approximately 5am to 6am tomorrow morning whereafter the showers will subside".
The City of Cape Town advised residents on Wednesday to not use more water just because it was raining, reminding them that the use of water was still officially for essential use only.
But the Western Cape government's James-Brent Styan says there have not been any fatalities reported yet.
Tourism sites and schools have been closed including the University of Cape Town in anticipation of the storm.
The cold front is expected to continue into Thursday, with no significant rainfall predicted for Friday.
"Our primary concern is the safety of learners and staff", says Brian Schreuder, head of Education Western Cape.