The driver, who had a weapon inside the car, was knocked unconscious and is seriously injured, French media report.
Police say the situation is now under control, and neither law enforcement officers nor civilians were injured.
France is under a state of emergency after being hit by a wave of deadly terror attacks in recent years.
A policeman was shot dead and two others were wounded in an attack on the Champs Élysées in April, just days before the presidential election.
French media, quoting police sources, say the incident earlier today was deliberate.
The national police Twitter account had earlier said (in French) that there was an "ongoing police operation", warning people to respect the security cordon.
The anti-terrorist section of the prosecutor's office has opened up an investigation.