A local mayor said one person was killed and several injured in the attack, but police could not immediately confirm the death or the number of injured people.
The mayor, Vincent Jeanbrun, told broadcaster BFM-TV that the attacker assaulted people in a park in Villejuif, then fled to a shopping centre in the area, L’Hay-les-Roses, and was shot by police there.
Police union official Yves Lefebvre said officers fired repeatedly because they feared the man was wearing an explosive belt and might blow himself up.
Interior Ministry officials and many police were at the scene on Friday afternoon.
Casualties have reportedly been taken to local hospitals, their condition has not yet been confirmed.
Local roads surrounding the park have been closed as police continue to investigate the incident.