Gerard Collomb told reporters that the man's motives were not immediately clear.
Bomb squad officers are at the scene on the city's most famous avenue, which is popular with tourists.
France's anti-terrorism prosecutor has opened an investigation into the incident.
No police officers or passers-by were hurt, the Paris police department said.
Two police officials said that a handgun was found on the driver, who they said was badly burned after the vehicle exploded.
The incident is the second this year on the city's most famous avenue.
An attacker defending Islamic State shot and killed a police officer on the Champs-Elysees in April, days before a presidential election, prompting an extensive security operation.
France is under a state of emergency after a string of deadly Islamic extremist attacks.
On Monday, police cordoned off a broad swathe of the Champs-Elysees avenue that cuts through central Paris, warning people to avoid the area.
Eric Favereau, a journalist for Liberation newspaper who was driving a scooter behind the gendarmes, said he saw a car blocking the convoy's path, then an implosion in the vehicle.
Mr Favereau wrote that the gendarmes smashed open the windows of the car while it was in flames and dragged out its occupant.
Other gendarmes used fire extinguishers to put out the flames.
The attacker was a 31-year-old man from a Paris suburb who had been flagged for extremism, police officials said.
They identified the man as from the suburb of Argenteuil, and said he had an "S'' file, which means authorities had been aware of potential links to extremism.
The interior minister said the incident shows the threat is still very high in the country and justifies the state of emergency.
Mr Collomb said he will present a bill on Wednesday at a cabinet meeting to extend the state of emergency from July 15, its current expiration date, until November 1.
He said the current situation in France shows a new security law "is needed" and the measure would "maintain a high security level" beyond the end of the state of emergency.
France has been under a state of emergency since the November 2015 attacks by Islamic extremists in Paris.
Visitors to an art exhibit of Auguste Rodin's works in central Paris were confined inside the Grand Palais for an hour after the attack.
Victoria Boucher and daughter Chrystel came in from the suburb of Cergy-Pontoise for a Paris visit and were not afraid to go to the famed avenue.
Chrystel said that "we were better off inside than outside".
But both agreed, as the mother said, "unfortunately we now are used to this".
"The show must go on," the daughter said in English. "They won't win."