Duduzane Zuma, a businessman, crashed his Porsche into a minibus taxi just before midnight on February 1 in the suburb of Sandton, the Sunday Independent, the Sunday Times and Eyewitness News radio reported.
Police confirmed an investigation of manslaughter against the Porsche driver, but declined to name the person until charges are laid and he appears in court.
"There was an incident where a Porsche collided in the rear of a taxi in the dark during heavy rain," said Johannesburg Metro Police spokesman Wayne Minnaar.
The fatality was 30-year-old Zimbabwean national Phumzile Dube, who was buried in her home country yesterday, the Sunday Times reported.
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"Zuma killed my wife and I want justice," said Themba Dube. "It doesn't matter whether he is the president's son- justice doesn't have eyes."
Taxi driver Vusi Dlamini was hospitalised after he collapsed at the scene.
"I don't like what happened. He bumped me out of the blue and my taxi overturned. One passenger died instantly," he told the Sunday Times.
Presidential spokesman Mac Maharaj told AFP he did not comment on Zuma family matters.
Duduzane, who turns 30 this year, is one of four children that Zuma had with his second wife Kate, who committed suicide in 2000.
Zuma currently has four wives and at least 21 children, some out of wedlock.
Duduzane Zuma has business relations with close family associates the Gupta brothers, and reportedly owns interests in their pro-government newspaper The New Age and ANN7 television news network.
The Gupta brothers, originally from India, made headlines last year when they landed a plane filled with wedding guests at a military airbase without proper authorisation.