Spokesperson of the French interior ministry Pierre-Henry Brandet told local broadcaster BFMTV that the police officers were "deliberately targeted", and the assailant was shot dead.
The gunman, armed with a machine gun, got out of a car and opened fire at the police in front of the store on the street, reports quoted a witness as saying.
He then began running away and injured two other officers before got shot in an exchange of fire with the police.
"We are asking all residents to avoid the Champs Elysees area in order to allow police operations to be carried out in serenity," said Brandet, adding that police investigation into the motive of the attack is underway.
The police are currently collecting statements from the various witnesses who were at the scene when the incident occurred, to verify the presence of a second assailant.
Meanwhile, the French prosecutors' office said the counter-terrorism office had opened an inquiry.
French President Francois Hollande will deliver a speech soon after an emergency meeting with Prime Minister Bernard Cazeneuve and Interior Minister Matthias Fekl.
Cazeneuve paid homage to the killed policeman and expressed solidarity with the injured on his Twitter account.
The Champs Elysees street was closed off shortly after the shooting, while a helicopter started patrolling the area.
Police vehicles with flashing lights were seen lining up along the street, and passengers were told to move away from the area. Concerns over security have been raised since Tuesday when two men were arrested for plotting an attack before the French presidential election, which is set to begin on Sunday.