"The child was found in a state of cardio-respiratory arrest at the bottom of the ship's pool," said Yann Bouvard, a spokesman for the maritime prefecture in the port of Brest.
French sea rescue services were alerted just before 2:00 pm (1200 GMT) and a medical team was dispatched by helicopter to the Independence of the Seas, a cruise ship belonging to the US company Royal Caribbean Cruise Line (RCCL) which sails under the flag of the Bahamas.
Two hours later, the child was transferred to the Morvan hospital in Brest where his condition was described as "grave".
The Independence of the Seas is a 338-metre vessel with four pools on board which is capable of carrying up to 3,600 passengers, according to the company's website.
The boy’s parents are believed to have flown with the boy to be by his side in the hospital in Brittany.
The circumstances around how the boy came to be lying at the bottom of the pool are still unknown but an investigation will be launched to find out what happened.
Speaking to the Times newspaper the head of the coast guard Bouvard described the incident as “incomprehensible”.
“What is terrible is that children can drown without making any noise at all.
“We’ve never had a case of a child drowning on a cruise ship before, but we have unfortunately, a lot of experience of that happening in pools on land and we know that it can happen to anyone, anywhere.”
Last summer authorities in France had to issue warnings to tourists and beachgoers after scores drowned across the country during the holiday period.
After seven men drowned off the Mediterranean coast in one day last week, local safety official Sebastien Royer told The Local: "It's very dangerous to ignore the rules. What happened on Sunday was rare. It was not normal for that to happen in one section of the coast. The winds and the currents created the rough seas.
"Those kind of weather conditions are more common in winter but they can easily occur in summer.
"Holiday makers are more at risk because because they don't know the sea, like locals do. People who live here know it can be dangerous but often holidaymakers think it is completely safe to swim in the Mediterranean.
"Surfers had been issued with warnings, but they still want to go out looking for waves,” he added.