The attacker was killed by authorities, but not before stabbing one person to death and leaving two victims "gravely injured" while two others were "lightly injured", according to CNN.
The alleged assailant was shot by the police and was pronounced dead.
According to BFM TV, an unidentified person attacked bystanders with a knife in the center of Paris on Saturday. The motivation for the attack has not been determined.
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". Please only share information coming from a trusted source.
The attack took place on Rue Monsigny in the second arrondissement, an area that lies between the main opera house and the Louvre museum, two major tourist attractions.
Authorities are working to identify the assailant and anyone who might have helped him, Collomb told reporters Sunday.
Police said two of the injured were "seriously wounded", while the other two were "slightly" hurt. "My first thoughts are with the victims of this odious act", he tweeted.
The attack comes as France is under a constant threat from terrorism.
Paris has been under higher security in recent years after a string of deadly terror attacks throughout Europe, many of which were claimed by the Islamic State.
The Islamic State group's news agency claimed that the man was a "soldier" of its extremist attack.
"Tonight, our city has been bruised", Paris mayor Anne Hidalgo wrote on Twitter in French after the attack.
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.
Citing local media reports, nydailynews.com stated that the attacker, a north-African man in his mid-twenties, shouted "Allahu Akbar" while carrying out the attack.
A motive was not immediately clear.