The incident is understood to have occurred in the Place de la Concorde at 8am on Sunday morning as barricades were beginning to go up in preparation for the race's finale in the French capital.
Reports indicate there is no suggestion of terrorism as a motive, but police are now searching for the driver and a passenger after the car failed to stop when fired upon, US-based Entertainment and Sports Programming Network, ESPN, reported on Sunday.
Team Sky's Chris Froome is set to become the first Briton to win the Tour de France twice when he arrives on the nearby Champs-Elysees later on Sunday afternoon.