A 34-year-old man and a 54-year-old woman were seriously wounded and rushed to hospital.
The attacker was slain by police after stabbing a 29-year-old man to death and injuring four others in a lively neighborhood near the Opera Garnier on Saturday night.
This woman describes how it began, in an area full of shops and restaurants.
Police shot and killed the man shortly after being alerted to the attack on the Rue Monsigny, a lively neighbourhood of theatres and restaurants near the main opera house in Paris. The motive or reason for the attack was unclear.
French interior minister Gerard Collomb tweeted: Aggression to #Paris: I salute the cool composure and responsiveness of the police forces that have neutralised the assailant.
" Based upon testament of eyewitnesses who stated they heard the enemy stating' [Allahu] Akbar' and because of the approach of the attack it's the anti-terror system who supervises of the examination", he stated.
In an online statement, the media wing of ISIS claimed responsibility for the attack.
Paris police officers evacuated people from some buildings in the Right Bank neighbourhood after the attack.
France's BFM tv interviewed an unnamed witness in a restaurant who stated a younger lady was on the entrance when "a person arrived and attacked her with a knife".
He said the four people injured were recovering and "out of danger" and that authorities were working to identify the suspect along with anyone who may have helped him.
The agency reported that Saturday night's attack was in response to ISIS' call for supporters to target allies of the US-led coalition to eliminate the extremists from Iraq and Syria, according to the Associated Press.
"Then the bartenders told us to come inside very quickly. My first thoughts are with the victims of this heinous act".
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.
France's military has been active in the coalition since 2014, and IS adherents have killed more than 200 people in France in recent years.