The hit-and-run occurred at around 2.30pm on Boulevard de Ménilmontant, in the city's 11th arrondissement.
The child, a member of the Roma community according to reports in the French press, was crossing a pedestrian crossing at the time when he was hit by a vehicle.
The driver of the van fled on foot with a fellow passenger, witnesses said, after reportedly surveying the scene of the crash in shock.
Emergency services were quick to arrive but were unable to revive the boy. He was pronounced dead at the scene.
(The Boulevard de Ménilmontant. Photo: France TV Info/Screenshot)
The exact circumstances of the accident remain unclear, with the Libération newspaper reporting that the child and his family were fleeing from police at the time.
The paper reported that the boy's family had been selling clothes at a Metro exit and were on the run after seeing police nearby.
This version of events was immediately denied by police.
A police source told the Europe1 radio, however, that no police investigation was ongoing in the area at the time, and that officers didn't actually arrive until ten minutes after firefighters showed up.
Paris Mayor Anne Hidalgo offered her condolences to the family of the victim, adding that she had faith the police would be quick to solve the crime.
One witness, an actress called Dominica, told Liberation that the tragedy highlighted the need to help families who were making a living on the streets.
"The police and these clothes sellers are playing cat and mouse every day," she said.
"I don't understand why they're not left alone... if we could just let them do it once or twice a week this kind of accident might not happen again."