The person who stabbed five people in Paris on Saturday night, killing one, yelled the Arabic phrase "Allahu Akbar," meaning "God is great," during the attack, city prosecutor François Molins told reporters at the scene.
Authorities have opened a terrorism investigation, he said.
Four people were wounded during the knife attack in the touristy 2nd arrondissement, or district, of Paris. It happened around 9 p.m. (3 p.m. Eastern), a time when streets and sidewalks were filled with people.
Two of the victims were gravely wounded and two others were lightly injured, police said.
The attacker, who French President Emmanuel Macron called a terrorist, is dead, according to police.
An official with the union for French police officers said officers first tried stun guns on the attacker but they didn't work, so police shot him as he came at them.
The media wing of ISIS claimed responsibility for the attack in a statement published online.
The Amaq News Agency said "the person who executed the stabbing in Paris is a soldier of the Islamic State." The statement also said the assailant acted in response to calls to attack anti-ISIS coalition countries.
ISIS did not provide proof to substantiate the claim and no authorities or security sources have yet verified the authenticity of the ISIS claim.
Macron said he salutes the courage of the police who "neutralized the terrorist" in the Paris knife attack, according to a tweet from his official account Saturday. He says his thoughts are with the victims.
French Interior Minister Gerard Collomb praised the cool and quick response by French police who "neutralized" the assailant.
"My first thoughts are for the victims in this odious attack," added Collomb, who made the comments via Twitter.
Paris Mayor Anne Hidalgo saluted the courage and professionalism of police, writing on Twitter that they have "again saved lives" and "have all my gratitude."
She also thanked the emergency services who arrived to the attack scene quickly and took charge of the wounded.
The location of the attack is about 10 minutes away by foot from the Paris opera house, known as Palais Garnier.