At least eight people have been reportedly injured, including two seriously and two have died, local media outlets have reported.
Paris Mayor Anne Hidalgo also offered her prayers and said she wanted the victims to know "all Parisians are by their side".
The Islamic State group claimed the attacker as one of its "soldiers".
Paris police officers evacuated people from some buildings in the Right Bank neighborhood after the attack, and bar patrons and opera-goers described surprise and confusion.
Police first tried to stop the attacker with a stun-gun before shooting him dead, according to the BBC.
We will remind, earlier it was reported that due to the attack of a man with a knife in Paris (France), two of the injured are in critical condition, one person was killed.
French prosecutor Francois Molins said the police's anti-terrorism unit would launch an investigation, given the aggressor's "mode of operation".
The knifeman shouted "Allahu akbar" as he attacked people in the Opera district, French prosecutors said.
The Aamaq statement did not provide evidence for its claim or details on the assailant's identity.
France "will not yield an inch to the enemies of freedom", Macron said on Twitter.
Inside Minister Gerard Collomb denounced the assault in a tweet, which translated as, "My first ideas are with the victims of this odious act".
France's BFM tv interviewed an unnamed witness in a restaurant who stated a younger girl was on the entrance when "a person arrived and attacked her with a knife".
Aggression in Paris: I salute the chilly blood and responsiveness of the police forces who neutralized the assailant.
Paris has been under extra security in recent years after a string of deadly Islamic extremist attacks.
"Five people in the 2nd district of Paris were attacked by an individual armed with a knife", Xinhua quoted a tweet by the prefecture as saying.
The suspect has yet to be identified, and the motive for the attack remains unclear.