Police said a terrorist motive was not suspected, but the violence added to tensions as Paris prepares to host the Games from July 26.
Police shot the man after he wounded an officer near the Champs-Elysees avenue on Thursday evening, police sources told AFP.
Paris police prefect Laurent Nunez said staff at a Louis Vuitton boutique had reported the man to be armed with a knife and had asked officers to intervene.
He said the man resisted and tried to flee, turning on the officers when they caught up with him and wounding one with the knife.
Nunez told reporters the officer was seriously injured to the neck but his life was not in danger.
He said there was no known “terrorist motive at this stage, and no link to the Olympic Games”.
A source in the prefecture said the attacker was a Senegalese national and was previously known to police.
A source in the prosecutors’ office later told AFP the man had died and added that a criminal investigation had been launched into the attack on the officer.
Tight Olympic security
Near the scene of the attack, a bomb disposal truck and several police trucks were parked, an AFP journalist saw. Crime-scene tape encircled the entire area.
France is on high alert ahead of the Games, having been the victim of numerous terror attacks in recent years.
On Wednesday evening, a motorist ploughed a car into a cafe terrace in northern Paris, killing one person and seriously injuring several others.
Prosecutors said the driver was committed for psychiatric treatment.
On Monday, a soldier was stabbed in the back by a 40-year-old man at a major train station in northern Paris.
Officials said the soldier’s life was not in danger.
Thousands of security personnel locked down a six-kilometre (four-mile) stretch of central Paris on Thursday ahead of the Olympics opening ceremony.
Officials say 35,000 police officers and 18,000 soldiers will provide security for the Games.
More than 300,000 spectators are expected to watch the opening ceremony along the banks of the Seine.
It will be the first time a Summer Olympics has opened with a ceremony outside the main athletics stadium.
National anti-terrorism prosecutor Olivier Christen on Tuesday said the Games “are not the subject of specific targeting by international terrorist organisations”.
Interior Minister Gerald Darmanin insisted Wednesday there was “no credible threat” against the Games at this stage.
