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 or buggy 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, told AFP: "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 on his profile on the photo blogging platform 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 – this is a difficulty we have in particular with Jehovah's Witnesses – we just want to contact them to try and see what happened."
French authorities told AFP the family arrived on Thursday night with their seven children and were driving a grey Hyundai registered KP60 HWK.
It was unclear what motivated the family to take the boy away.
Det Supt Dick Pearson, of Hampshire Constabulary, said: "If we do not locate Ashya today there are serious concerns for his life.
"He is receiving constant medical care within the UK due to recent surgery and ongoing medical issues. Without this specialist 24 hour care, Ashya is at risk of additional health complications which place him at substantial risk.
"He needs to be taken to a medical facility for his urgent health requirements as soon as he is located."