French President Francois Hollande said he believes the attack is terror-related, though officials have stopped short of saying so.
One police officer and the attacker were killed in the incident.
French Interior Ministry spokesman Pierre-Henry Brandet said on BFM television that a man emerged from a auto and opened fire on a police vehicle.
Police have also issued an arrest warrant for a second suspect in the shooting, according to a document obtained by Reuters.
He said: "I thought they were firecrackers". In fact, he (the gunman) was hidden behind the van and shooting at the police.
Witness Ogur Yilmaz told Eleanor he was leaving a cafe when he heard "two or three shots" and saw people fleeing. "As soon as the policeman opened the door of the van, he fell".
He was then shot dead by security forces.
An interior ministry spokesman said it was too early to say what the motive was for the attack.
French police tweeted, "Police intervention underway in the area of the #ChampsElysees avoid the sector and follow the instructions of the police forces".
The state of emergency was recently extended until the 2017 French elections are done on Sunday, May 7. The majority of those attacks had been claimed by the Islamic State.
The Interior Ministry spokesman said the officers were deliberately targeted and the police union added that the man was killed while sat in a auto at a red light.
Media had initially reported that at least two attackers were involved.
Police said the attacker was shot dead by an officer or officers.
The attack comes three days before hotly contested presidential elections in France.
"What can you say?"
He calls the attack a "terrible thing" and says "it never ends". "We have to be strong and we have to be vigilant".
Police and soldiers sealed off the area, ordering tourists back into hotels and blocking people from approaching the scene.
Police cars filled surrounding streets and the neighbourhood was evacuated.
President Donald Trump says Thursday's fatal shooting in Paris "looks like another terrorist attack". It was unclear if the two were linked.
BFMTV was the first to report the shooting on one of the Paris' most famous boulevards.
Police union spokesperson Yves Lefebvre from Unité SGP Police said officers were raiding the suspect's residence in Chelles, Seine-et-Marne.
France has been plagued by terrorism since the horrific attacks of November 2015 that left 130 people dead and hundreds injured.