The incident took place on Wednesday on the Quai Voltaire, a road embankment on the opposite side of the River Seine from the Louvre.
A verbal clash between the driver of the hop-on-hop-off sightseeing bus and the car driver degenerated into a fight.
The bus driver then got back into his vehicle, drove towards the motorist and crushed him against another bus. He died at the scene.
In Rome, a chronic lack of maintenance and an ageing fleet means that buses have an unfortunate habit of bursting into flames.
The latest incident happened in the city centre a week ago, when an electric bus caught fire and all the passengers had to be evacuated.
Dozens of buses in the capital have gone up in smoke. Last May, a bus burst into flames in Via del Tritone, a shopping street which lies between the Spanish Steps and the Trevi Fountain, both popular tourist attractions.
Passengers managed to get off the bus before it was engulfed in flames and no one was hurt.
The fire was reportedly caused by a short-circuit. As the heat built up, windows exploded in front of crowds of onlookers.