Jolidee Matongo had been campaigning with Mr Ramaphosa before the accident.
His vehicle collided with a van while trying to avoid a pedestrian who had run on to the road, local media report.
The pedestrian and the other vehicle's driver also died, while Mr Matongo's two bodyguards are being treated in hospital for their injuries.
Mr Matongo only became mayor on 10 August following the death of his predecessor from Covid complications.