Islamic State claimed responsibility for the attack via its Amaq news agency, but provided no proof for its claim.
"I was taking orders and I saw a young woman trying to get into the restaurant in panic", Jonathan, a waiter at a Korean restaurant, told AFP.
A terrorist investigation has since been launched.
Paris police officers evacuated people from some buildings in the Right Bank neighbourhood after the attack, which happened on rue Monsigny at about 9 p.m. (1900 GMT.) Bar patrons and opera-goers described surprise and confusion in the immediate area. There is no known motive for the attack at this time.
The attacker was neutralized by police, said Interior Minister Gerard Collomb.
Later the IS group said it was behind the attack, in a brief statement posted on its news outlet.
The brothers behind the Boston Marathon bombing in 2013, Tamerlan and Dzhokhar Tsarnaev, had Chechen links and Turkish authorities said a Chechen jihadist was the suspected organiser of an attack on Istanbul airport in 2016 that killed 45 people.
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He also said that while Boeing's prospects for the 777 and the 777X are indeed cause for concern, "it's not much to do with Iran". But for some of those companies, those deals could turn into losses if the new sanctions require them to cancel transactions.
The claim was not substantiated and French officials outright didn't say the attack was linked to the terrorist group.
Among the four hospitalized, two were in grave condition and two others sustained minor injuries. The statement also said the assailant acted in response to calls to attack anti-ISIS coalition countries. A friend came to her aid and the attacker left, "hitting on all the doors, all the shops", the witness told BFM.
"All my thoughts are with the victims and wounded of the knife attack perpetrated in Paris tonight, as well as their loved ones", he added.
The bloodbath follows a series of ISIS and Al Qaeda attacks in France which has seen nearly 250 killed by terrorists since early 2015.
The attacker was then shot by officers and later confirmed lifeless, Paris police stated.
He said a woman, stabbed by the attacker, ran into into the restaurant bleeding.
The mayor of Paris Anne Hidalgo expressed his condolences to the relatives of the deceased and wounded, saying that all Parisians feel sorry for them.
Paris has been under higher security in recent years after a string of deadly Islamic extremist attacks.