The incident happened on the Champs-Elysees this afternoon and led to a section of the famous boulevard being evacuated.
The attacker was a 31-year-old man from a Paris suburb who had been flagged for extremism, police officials said.
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.
France has been under a state of emergency since a series of terror attacks in November 2015.
The bomb squad arrived at the scene and an explosives-detecting robot has been pictured inspecting the attacker's dead body. According to reports, a vehicle crashed into a police van before going up in flames.
Interior Minister Gerard Collomb said the man's auto was carrying weapons and explosives that could have caused a blast.
No one else is thought to have been injured in the horrifying attack which counter-terrorism are now investigating.
Earlier, Interior Ministry spokesman Pierre-Henry Brandet said the suspect deliberately drove his auto - a Renault Megane - into the military van, which was on move at the time, and then he began shooting at around 3.40 p.m. local time (1340 GMT).
There were no immediate reports of police officers being injured in the incident.
It is unclear why the attacker, who has been arrested, drove into the police.
Reports suggest the attacker was badly burned.
The suspect is wearing a white shirt and dark shorts and prone on his stomach on the avenue.
Police have closed two of the subway stations on the Champs-Elysees, a major tourist draw in the French capital.