The assailant died in the incident, although investigators offered no immediate details about the cause of his death. There was no early claim of responsibility for the assault.
The attack - which occurred just a short distance from where a jihadist shot dead a police officer, two months earlier - was carried out by an individual who had been on France's security watchlist since 2015 for membership of "the radical Islamist movement," sources close to the probe said.
They identified him as Djaziri Adam Lotfi, who had been raised in the hardline Salafi Islamic ideology, and did not have a criminal record.
Interior Minister Gerard Collomb said a car hit the leading vehicle in a line of police vans as they headed down the Champs-Elysees, near the Grand Palais exhibition hall.
"The security forces have been targeted in France once again," he said.
Ministry spokesman Pierre-Henry Brandet said the car, a white Renault Megane, caught fire.
Video showed a thick orange smoke pouring from the car after the impact as the vehicle sat in the middle of the prestigious avenue which is lined with shops and cinemas.
Police sources told AFP that they found a Kalashnikov assault rifle, two handguns as well as a gas bottle on the car.
The "arms, explosives... could potentially blow this car up," Collomb said. Sources previously told AFP that there were multiple gas bottles in the car.
No police or bystanders were injured in the incident, which occurred near the Grand Palais exhibition hall.
"People were running every which way," said a 51-year-old bystander who gave his name only as Alexandre. "Some shouted at me to get away."
Police closed two of the Metro stations on the Champs-Elysees, but two hours after the attack tourists were back taking selfies of the Arc de Triomphe and visiting shops.
Collomb said the attack "shows once again that the threat (of an attack) remains extremely high in France".
The incident occurred almost two months to the day after a policeman was shot and killed nearby in the runup to the first round of France's presidential election.
Also read: Woman 'slapped' car before Damond shot
The gunman, Karim Cheurfi, was shot dead by police and a note praising the Islamic State group was found next to his body.
On June 7, a hammer-wielding Algerian man was shot and wounded by police after he struck an officer on the head in front of Notre Dame cathedral in Paris, shouting it was in revenge "for Syria".
He had pledged allegiance to the Islamic State group in a video found at his home.
A man on the radar of French authorities was killed Monday after ramming a car carrying explosives into a police vehicle in Paris.
Earlier Monday, a van ploughed into a crowd of Muslims near a London mosque, injuring 10 people.
Two weeks ago jihadists used a van and knives to crush and stab to death eight people enjoying a night out around London Bridge. Three of the victims were French.
In May, a suicide bomber killed 22 people, including children, at a concert by US singer Ariana Grande in Manchester.
France remains under a state of emergency imposed after the November 2015 attacks in Paris, when Islamic State jihadists slaughtered 130 people in a night of carnage at venues across the city.
Previous major attacks targeted the Paris offices of the Charlie Hebdo satirical magazine in January 2015.
A senior police officer and his girlfriend were both killed by a radicalised man at their home in the Paris suburbs a year ago.
And in July last year, a radicalised Tunisian man knocked down and killed 86 people as he rammed a truck through a crowd watching Bastille Day fireworks in the Riviera city of Nice.
On Wednesday, the French government is to unveil a new anti-terrorism law, designed to allow the state of emergency to be lifted.
"To those who question the necessity of such laws, you can see that the state of France today necessitates it," Collomb said.
"If we want to effectively ensure the security of our citizens, we must be able to take a certain number of measures," he added.