Paris police said the man was armed with a knife and a metal bar, and first attacked four people outside a cinema in the 19th district of Paris.
Of the seven wounded, four are in a critical condition, police said. Quai de la Loire runs alongside the popular Villette Canal Basin and boasts a number of restaurants and cinemas.
There has so far been no initial indication the assault was linked to terrorism, according to French authorities.
Police have so far said it was not a terrorist incident, and a man is reportedly in custody.
The victims were all rushed to local hospitals, where their conditions were described as "serious but not life threatening".
Witnesses told Agence France Presse the man was also carrying an iron bar.
The suspect is believed to be an Afghan national and has been arrested, said a source close to the inquiry.
Two British tourists, an Egyptian tourist and a local man were among the injured, police added.
"Around four or five balls hit him in the head, but they weren't able to stop him". A man is said to have been arrested over the knife spree.
Police said investigators had "very quickly" dismissed a terrorist motive after the August 13 incident.
While the motives for the attack remain unclear, a judicial source said it did not appear to be akin to other attacks carried out by Muslim militants in Paris in recent years. "Loads of people arrived, some were saying "kill him" but one guy who was pinning him down said 'no, the last thing we must do is kill him'".
In June, a woman stabbed two people with a box cutter in a supermarket in Toulon.