PARIS—A man stabbed a person to death in the streets of central Paris on Saturday evening and wounded four others, in an assault that French investigators were treating as a terrorist attack.

Police shot and killed the man shortly after the attack began, French authorities said. Paris prosecutor François Molins said the man yelled “Allahu Akhbar!”—“God is great” in Arabic—during the stabbing, indicating the attack was the latest in a string of assaults committed by Islamist extremists in France.

Islamic State quickly claimed the assault via its Amaq media service, calling the assailant a “soldier” of the extremist group.

The attack took place near the Palais Garnier, the opulent Parisian ballet and opera house, a neighborhood packed with restaurants and bars. French investigators were trying to identify the man, who wasn’t carrying identification documents, a judicial official said.

France has been on high alert since January 2015 when gunmen killed 17 in the Paris region, including 12 at the satirical newspaper Charlie Hebdo. In November 2015, a team of militants sent by Islamic State from territory it then controlled in Syria killed 130 people in and around Paris, one of the worst terrorist attacks in European history.

Since then, France has suffered a series of attacks by assailants with limited or no known operational connections to Islamic State or other extremist groups. These assailants have instead been inspired by Islamic State propaganda calling for attacks on French soldiers, police and civilians.

“France once again pays the price of blood but won’t give an inch to the enemies of liberty,” French President Emmanuel Macron said on Twitter.

Most recently, a Moroccan-born man in March killed four people in southern France. One of the victims, French gendarme Lt. Col. Arnaud Beltrame, was shot and killed after trading himself for a hostage the gunman was holding at a supermarket, prompting an outpouring of tributes from nations around the world.

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Write to Matthew Dalton at Matthew.Dalton@wsj.com

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