The Paris prefecture had earlier said a person had carried out a knife attack in the second arrondissement - or district - of the French capital.
French Prime Minister Edouard Philippe said police were on the scene "within five minutes" of the attack and that some nine minutes later the assailant was dead, he added.
"My first thoughts are for the victims in this odious attack", added Collomb, who made the comments via Twitter.
A wave of attacks, claimed by the Islamic State (IS), had broken several times the calm at home with the bloodiest was in Paris where a series of explosives and shootings left 130 victims in November of 2015.
Paris police officers evacuated people from some buildings in the Right Bank neighbourhood after the attack.
One person has died in the attack, in which three other people have been injured, BFM TV said.
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.
The Amaq News Agency said "the person who executed the stabbing in Paris is a soldier of the Islamic State".
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France has become a major target of frequent terrorist attacks in recent years.
France has "paid once again the price of blood but will not cede an inch to the enemies of freedom", French President Emmanuel Macron said in a statement.
The four others injured in the attack were hospitalized.
The attack occurred in central Paris, near the Opera Garnier.
Prosecutor Francois Molins said an anti-terrorism unit would launch an investigation.
The motive for the attack was not immediately known.
The identity of the man and the reason for the attack are unclear.
Authorities are working to identify the assailant and anyone who might have helped him, Interior Minister Gerard Collomb told reporters Sunday.