A source close to the investigation said the suspect, believed to be an Afghan, was arrested.
"Nothing at this stage shows signs of terrorist nature in these assaults," the source said, adding that the attacker had targeted "strangers on the street."
Of the seven injured, four are in critical condition, police said.
The incident occurred just after 11:00 pm (2100 GMT) on the banks of a canal in the northeast of the capital.
A security guard in one of the two cinemas on either side of the Bassin de la Villette, part of the Canal de l'Ourcq, said he saw a man who had already assaulted people being chased by two other men who tried to stop him.
"He had an iron bar in his hand that threw the men who were chasing him, then he took out a knife," he told AFP.
Another eyewitness, Youssef Najah, 28, said he was walking down the canal near a bowling alley when he saw a man running and holding a knife about 25-30 cm (10-11 inches) long.
"There were about 20 people chasing him, they started throwing petanque balls at him," Najah said, referring to popular sport in France, also known as petanque.
"Around four or five balls hit him in the head, but they could not stop him," he added.
According to the same witness, the attacker dived into an alley, where the man "tried to hide behind two British tourists." We said, "Careful, he has a knife." But they did not react.
The couple was attacked, he said.
According to a judicial source, a police investigation was initiated for attempted murder.
It is the last of several knife attacks that France has seen in recent months, with terrorism ruled out in most cases.
On August 23, a man stabbed his mother and sister to death and seriously injured another person in a town near Paris before being shot to death by police.
The reason for the violence was not clear despite the fact that the Islamic State (IS) group claimed that it was an attack by one of its fighters in response to the propaganda of the terrorist organization.
Authorities said the 36-year-old man had serious mental health problems and had been on a terrorist watch list since 2016.
That attack came days after an Afghan asylum seeker was arrested in the city of Perigueux by a drunken assault with a knife in which four people were injured, one of them seriously.
Police said investigators had ruled out "very quickly" a terrorist motive after the Aug. 13 incident.
And on June 17, two people were injured in another southern city when a woman who shouted "Allahu akbar" (God is the best) attacked them in a supermarket with a knife cut.
France has been on high alert after a series of jihadist attacks in recent years, often by people who have become radicalized or who claim to have acted on behalf of the IS group.
More than 240 people have been killed by Islamic extremists since a massacre in the Charlie Hebdo satirical magazine in Paris in January 2015.