Police have launched an operation to find the vehicle which left the scene after the accident.
According to the French police, four people sustained minor injuries and two individuals have more serious injuries.
The injured soldiers belong to Operation Sentinelle, an operation introduced in the wake of the terrorist attacks in 2015.
Reuters quotes Levallois Mayor Patrick Balkany as saying that a there is "no doubt it was a deliberate act." He described the incident as "an odious act of aggression".
On July 14, 2016, a terrorist in a truck rammed into a crowd watching Bastille Day fireworks in the southern city of Nice, leaving 86 people dead.
SPUTNIK/MNA