The vehicle, a dark BMW auto, hit the soldiers at Place de Verdun in Levallois-Perret at the northwestern edge of Paris on Wednesday at about 8:00 a.m. local time (0600 UTC).
Authorities checked video surveillance of the area, near the city hall of Levallois, northwest of Paris, and police fanned out around the French capital and stopped numerous cars as they searched for the attacker.
He said a BMW was parked near the soldiers' barracks and appeared to be waiting for them to come out.
The vehicle used to slam into the soldiers was a BMW, said French TV news channel BFM, adding that the injured soldiers have been transported to Percy military hospital in Clamart near Paris.
Franceinfo spoke to the mayor of Levallois-Perret, who condemned the possible attack against military personnel in the commune.
Levallois-Perret is about 5 kilometers from the center of Paris.
The latest incident is one of several recent attacks targeting French security forces guarding public sites.
"It's an odious act of aggression", Balkany also said, adding that the vehicle in question was a BMW.
"It all happened very quickly", he said.
Two people were seriously injured and four others were less badly hurt, a spokesman said. Quoting unnamed police officials, however, the AP said a man was arrested at one stop. "It hurtled at them.it accelerated rapidly".
Police are now hunting for the driver and the vehicle, a BMW, a Paris police spokesman told the Associated Press. "The ongoing probe will determine his motives and the circumstances in which he acted", Parly added.
The city has sustained about a dozen terror attacks since the November 13, 2015, assaults by Islamic State militants that killed 130 people.
A man wielding a knife was arrested on Saturday after trying to force his way through a security checkpoint at the Eiffel Tower.