This emerged after the drivers of the two vehicles - a Hyundai Elantra and a minibus taxi - were arrested in connection with their alleged roles in the fatal incident.
The minibus taxi rammed into the Hyundai, forcing it off the road. The Hyundai then hit the cyclist, killing him.
Ekurhuleni Metro Police spokesman Inspector Kobeli Mokheseng said: "Because of the road-rage, both drivers were arrested and will be charged with reckless and negligent driving. A case of culpable homicide has also been opened to see whether anyone should be held liable for the death."
The cyclist was apparently on his way to work when he was killed.
The 29-year-old Hyundai driver allegedly told the driver of the white Toyota Siyaya that he was driving recklessly. The Hyundai was carrying four people - the driver and three girls aged between nine and 12.
Olga Mhlaba, who was in the area when the accident occurred, said the fight began at a petrol station a few metres from the crash.
The two drivers continued exchanging harsh words down the road. The taxi driver apparently lost his temper and rammed into the righthand side of the Hyundai, causing it to crash into a tree.
Nick Smith, a construction worker, said the accident happened in the blink of an eye.
"It was so quick, no one saw it. The lady behind them stopped and phoned the police," he said.
The ambulance arrived within 15 minutes. Paramedics found the cyclist in a critical condition. He died on the scene.
South African National Taxi Council spokesman Thabisho Molelekwa said taxi drivers should know there were consequences for their actions.
"If the driver in question is found guilty of intentionally causing the accident, there will be dire consequences. Taxi drivers need to know where to draw the line," he said.
The two men will appear in the Alberton Magistrate's Court soon.
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