Two of the victims were gravely injured and two others were lightly injured, according to police.
Among the four hospitalized, two were in serious condition and two others sustained minor injuries.
France has suffered a series of major Islamist attacks including the massacre at the satirical newspaper Charlie Hebdo, the November 2015 attacks that killed 130 in Paris, and the 2016 Bastille Day truck attack in Nice that killed more than 80.
Islamic State's propaganda arm has described the suspect in the attack as one of its "soldiers".
"My thoughts are with the victims of this abhorrent act", he said.
The attacker struck in a retail and dining precinct on Saturday night (local time).
A police officer cordons off the realm after a knife assault in central Paris, Saturday Could 12, 2018.
French authorities are denouncing the attack.
France has become a major target of frequent terrorist attacks in recent years. France's military is active in the US -led coalition against the Islamic State group in Iraq and Syria. France will not cede to the "enemies of freedom", he tweeted.
Shipping Will Have Time to Adjust to Iranian Sanctions
Now it's up to the Iranians and other countries involved in the deal to help the world stave off that unnerving possibility. Italy has long-established political and economic ties with Iran, and is its main trading partner within the EU.
The Islamic State group (ISIS) claimed responsibility, according to the SITE monitoring group.
France's military has been active in the coalition since 2014.
Saturday's attack occurred near many bars and theaters, as well as the opera.
Paris police have confirmed that the assailant has been killed.
One person has been killed and several injured in a knife attack in Paris, French media say. The alleged attacker was killed by police.
Interior Minister Gerard Collomb, writing in French on Twitter, praised the "responsiveness of the police forces who neutralized the assailant".
A motive was not immediately clear.
Paris police officers evacuated people from some buildings in the Right Bank neighbourhood after the attack, which happened on rue Monsigny at about 1900 GMT.
The police said that the attacker was armed with a knife, however, gave no additional particulars. The attacker is also dead, police tweeted. Authorities have not revealed the attacker's identity.