Air France said the plane sent a message at 0214 GMT saying it had an electrical short circuit after experiencing turbulence.
Brazil's air force said a search and rescue mission was under way near the island of Fernando de Noronha.
It added that the plane was well across the Atlantic when it disappeared, and the search had to cover a wide area.
French minister Jean-Louis Borloo said the plane had probably had an accident and ruled out hijacking.
An airport official told AFP the Airbus 330-200 had been expected to arrive in Paris at 1110 local time (0910 GMT).
Another official said it was possible that the plane had a transponder problem but this was very rare.
"We are very worried," he said, quoted by AFP news agency.
Crisis centre
Mr Borloo, the minister in charge of transport, said the plane would already have run out of fuel.
"By now it would be beyond its kerosene reserves so unfortunately we must now envisage the most tragic scenario," he said, quoted by Reuters news agency.
Flight AF 447 left Rio at 1900 local time (2200 GMT) on Sunday. It had 216 passengers and 12 crew on board, including three pilots.
An Air France spokeswoman said there had been no radio contact with the plane "for a while".
It is reported to have disappeared 300km (186 miles) north-east of the Brazilian city of Natal.
Brazilian air force spokesman Col Henry Munhoz told Brazilian TV it had failed to be picked up by radar on the Cape Verde Islands on its way across the Atlantic.
"Air force planes left Fernando de Noronha and are flying towards Europe to start the search for the missing plane," he said.
Airport authorities have set up a crisis centre at Charles de Gaulle.
An Air France official told AFP that people awaiting the flight would be received in a special area at the airport's second terminal.
French President Nicolas Sarkozy has been informed of the incident and has expressed his deep concern, his office said.
He has demanded that the relevant authorities do everything they can to find the plane and "shed light on the circumstances surrounding its disappearance as rapidly as possible".
This is the first major incident in Brazilian air space since a Tam flight crashed in Sao Paulo in July 2007 killing 199 people.
TIMELINE
Flight AF 447 left Rio at 1900 local time (2200 GMT) on Sunday
Airbus A330-200 carrying 216 passengers and at least 12 crew
Contact lost 0130 GMT
Missed scheduled landing at 1110 local time (0910 GMT) in Paris
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What a tradegy.
