A six-month-old baby was among the dead, and a three-year-old child was seriously wounded by the suspect before he was shot and injured by police.
One of two officers who were fired upon by the attacker died of his injuries.
The circumstances and motive for the killings near the town of Roye have yet to be established, police sources said.
The suspect is a member of the same travelling community, according to local deputy mayor Freddy Cantrel.
The suspected shooter was apprehended and arrested after being injured in the incident, according to BFMTV, and was taken to the University Hospital of Amiens.
Footage from the area appears to show a police helicopter scouting the scene. The area was surrounded by armed police and the attack happened near to a police station.
A large number of ambulances and helicopters rushed to the scene.
It is not yet known what caused the violence at the traveller camp.
However, police sources said the shooting is a criminal matter which is not linked to terrorism.