The vehicle, a BMW, was parked in an alley before it accelerated into the soldiers as they left their barracks to go on patrol, said Patrick Balkany, mayor of Levallois-Perret.
“The vehicle did not stop. It hurtled at them … it accelerated rapidly,” he told broadcaster BFM TV.
Armed Forces Minister Florence Parly said the driver was on the run and being sought, and an investigation was under way to determine “the motives and circumstances” for what she called a “cowardly act”.
A justice ministry official said counter-terrorism investigators had been assigned to the case.