Four people were wounded during the knife attack in the touristy 2nd arrondissement, or district, of Paris.
An eyewitness told broadcaster BFMTV that she had seen a young man running towards three policemen, who shot him down.
Mr Molins said the decision was made due to the style of the attack and on the accounts of witnesses who said the attacker cried "Allahu Akbar" (God is great in Arabic) during the incident.
A police official said the assailant didn't have identity documents with him during Saturday's attack but was identified thanks to DNA.
Hours later, the terrorist group Islamic State claimed responsibility for the attack via its propaganda agency.
Several attackers have used weapons such as knives or a hammer.
French President Emmanuel Macron praised officers for "neutralising the terrorist".
The area around the assault, in Paris' Second District has been locked down by police. He was then shot by the officers. "The police, fire brigade and ambulance arrived", one female witness told LCI television. The Islamic State group claimed he was one of their soldiers.
There have also been a string of less deadly but frequent attacks by lone wolf jihadists wielding knives or guns. Witnesses described scenes of panic as people out for a weekend night realized that a potential terror attack was occuring. France's military is active in the US -led coalition against the Islamic State group in Iraq and Syria.
Iraqi security forces have also recaptured nearly all the ground it held in that country, where it originated.
The four people injured are out of life-threatening danger, Interior Minister Gerard Collomb said.
"Police were quickly on the scene, in less than five minutes".
In October 2017, Macron signed an anti-terrorism law which he said was necessary to tackle the rampant terrorism in the country.
"Tonight, our city has been bruised", Hidalgo wrote on Twitter after the attack. My very first thoughts will be with the victims of this heinous act.
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