Ashya King's parents took him from a hospital in Southampton, southern England, on Thursday without doctors' consent and boarded a ferry to the French port of Cherbourg the same day, a British police spokesman said.
The spokesman said the boy's life was at "substantial risk" as he needed constant medical care following recent surgery, adding that he was likely to be in a wheelchair as he cannot move.
"We are working with our counterparts in France to activate their emergency child rescue alert procedures," he said.
Eric Bouillard, a prosecutor in Cherbourg, said: "We believe he was kidnapped given the circumstances of his departure from hospital as relayed to us by the British.
"For the moment, what we most want to do is contact the family," added Bouillard.
Ashya's brother Naveed King in his profile on the photo application Instagram describes himself as a Jehovah's Witness.
Jehovah's Witnesses refuse blood transfusions on religious grounds but are open to other medical procedures.
Bouillard said: "Even if we cannot treat children against their parents' wishes … we just want to contact them to try and see what happened."