The Islamic State group claimed the attacker as one of its “soldiers”.
Counter-terrorism authorities took charge of the investigation, and president Emmanuel Macron vowed that France would not bow to extremists despite being the target of multiple deadly attacks in recent years.
Paris police officers evacuated people from some buildings in the Right Bank neighbourhood after the attack, which happened on rue Monsigny at about 9pm. Bar patrons and opera-goers described surprise and confusion in the immediate area.
Beyond the police cordon, however, crowds still filled nearby cafes and the city’s night-life resumed its normal pace soon after the attack.
Prosecutor Francois Molins said counter-terrorism authorities were leading the investigation on potential charges of murder and attempted murder in connection with terrorist motives.
“At this stage, based on the one hand on the account of witnesses who said the attacker cried ‘Allahu akbar’ (God is great in Arabic) while attacking passersby with a knife, and given the modus operandi, we have turned this over to the counter-terrorist section of the Paris prosecutor’s office,” Mr Molins told reporters from the scene.
The Islamic State group’s Aamaq news agency said in a statement early on Sunday that the assailant had carried out the attack in response to the group’s calls for supporters to target members of the US-led military coalition squeezing the extremists out of Iraq and Syria.
The Aamaq statement did not provide evidence for its claim or details on the assailant’s identity.
France’s military has been active in the coalition since 2014, and Islamic State adherents have killed more than 200 people in France in recent years, including the 130 who died in the coordinated November 2015 attacks in Paris.
Mr Macron tweeted his praise for police who “neutralised the terrorist” and said “France is once again paying the price of blood but will not cede an inch to enemies of freedom”.
Paris police said the attacker in Saturday’s stabbings was armed with a knife and targeted five people in the 2nd arrondissement, or district, killing one and seriously injuring two. The other two suffered less serious injuries.
The attack occurred near many bars and theatres, as well as the opera.
France’s BFM television interviewed an unnamed witness in a restaurant who said a young woman was at the entrance when “a man arrived and attacked her with a knife”.
A friend came to her aid and the attacker left, “hitting on all the doors, all the shops,” the witness told BFM. He turned onto another street, and everyone scattered, the witness said.
Another witness described leaving the opera house and being told to go back inside because of the attack.
Interior Minister Gerard Collomb denounced the “odious attack”.