
The attack happened in the town of Villejuif, about 8km south of central Paris. Police cordoned off the area around the park, and the deputy head of the French interior ministry was at the scene talking to police officers.
Two of the victims are in grave condition in hospital, BFM TV quoted sources close to the investigation as saying.
There was no immediate word on the identity of the assailant, nor his motive.
Ambulances and police vehicles lined a road approaching the park, according to a Reuters journalist at the scene.
In the past four years, the French capital has been rocked by major attacks resulting in mass casualties.
In October last year, four people were stabbed to death at the Paris police headquarters by Mickael Harpon, an IT specialist working for the police.
Prosecutors said that attacker, who was shot dead by police, had come under the sway of radical Islamists.
Coordinated bombings and shootings by Islamist militants in November 2015 at the Bataclan theatre and other locations around Paris killed 130 people in the deadliest attacks in France since World War II.