The incident came as French voters prepared go to the polls on Sunday in the most tightly-contested presidential election in living memory.
Paris police spokeswoman Johanna Primevert told The Associated Press the attacker targeted police guarding the area near the Franklin Roosevelt subway station on Thursday night (Friday morning, NZ time).
The IS group claimed responsibility for the fatal shooting in a statement by the jihadists' propaganda agency Amaq.
A prosecutor said his identity had been been verified and police said at least one location in the eastern Paris suburbs was being searched.
France's interior ministry said the gunman was killed after opening fire on the officers at around 9:00 pm (1900 GMT) on the boulevard.
Brandit stopped short of calling the incident a terrorist attack, contradicting earlier reports that cited police sources. He said authorities are looking at many possible motives, and that terror investigators are involved in the case.
Parisians were warned not to approach the Champs-Elysées area after what the local police said was a likely terror attack.
"We had to hide our customers in the basement", Choukri Chouanine, manager of a restaurant near the site of the shooting, told AFP, saying there was "lots of gunfire". What can you say?
He calls the attack a "terrible thing" and says "it never ends".
Emergency vehicles blocked the wide avenue that cuts across central Paris between the Arc de Triomphe and the Tuileries Gardens, normally packed with cars and tourists.
The attack comes three days before the first round of France's tense presidential election.
A French television station hosting a televised event with the 11 candidates running for president briefly interrupted its broadcast to report the shootings. The far-left candidate Jean-Luc Melenchon said "No panic, let's not interrupt our democratic process to show that the violent ones will not have the last word".
France has lived under a state of emergency since 2015 and has suffered a spate of Islamist militant attacks that have killed more than 230 people in the past two years. It identified the attacker as Abu Yussuf al-Baljiki, suggesting he's from Belgium - details not confirmed by the French authorities.
Ministry spokesman Pierre-Henry Brandet said on BFM television that a man came out of a auto and opened fire on a police vehicle.