Levallois-Perret Mayor Patrick Balkany said the car, a BMW, was parked in an alley before it accelerated into the soldiers as they left their barracks to go on patrol duty.
Police said two of the six were seriously injured.
Speaking to broadcaster BFM TV, Balkany said that what he called a "disgusting" act of aggression was "without any doubt" premeditated.
"It all happened very quickly. The vehicle did not stop. It hurtled at them ... it accelerated rapidly." The soldiers were rushed to hospital, he added.
Police said a search for the driver and the vehicle, which they described as dark-coloured and probably a BMW, was under way.
It was parked on the edge of the Place de Verdun square in the centre of Levallois, which is situated on the western edge of Paris.
The area, quieter than normal in peak summer holiday season, was cordoned off after the incident, which happened at around 8am, police said.
Levallois-Perret is about 5 km from city centre landmarks such as the Eiffel Tower and the Elysee Presidential Palace.