"At around 0029 GMT (3:29 am) when it was in Egyptian airspace, the plane disappeared from Greek radars... it crashed around 130 nautical miles off the island of Karpathos," the source told AFP.
The official said the last communication with the pilot was three minutes before the plane disappeared, and that there had been no distress call.
The Greek defence ministry said it had dispatched two search planes and a frigate to the area.
EgyptAir had said it was informed by the military that it detected a "distress message" from the Airbus A320 which was en route from Paris to Cairo when it disappeared from radar screens.
Egyptian search teams combed the Mediterranean for signs of an EgyptAir flight that vanished from radar screens en route from Paris to Cairo on Thursday with 66 people on board, the airline said.
Twenty-six foreigners were among the 56 passengers, including 15 French citizens, a Briton and a Canadian, EgyptAir said.
France called a crisis meeting of top ministers as Prime Minister Manuel Valls said "no theory can be ruled out" to explain the plane's disappearance.
‘No distress call’
EgyptAir said contact was lost with the flight about 280 kilometres north of the Egyptian coast.
EgyptAir Holding Company vice president Ahmed Adel said there had been "no distress call" before it vanished, but the airline later said a "distress message" had been picked up by the military.
The Egyptian military said it had deployed search aircraft and naval vessels to locate the plane, in cooperation with Greece.
A tweet on the airline's official account said Flight MS804 left Paris at 11:09 pm heading to Cairo (and) has disappeared from radar".
Further tweets in Arabic said contact was lost at 2:45 am Cairo time (0045 GMT), when the plane was just inside Egyptian airspace and at an altitude of 11,000 metres (37,000 feet).
The airline said in a statement that Egyptian military search and rescue teams were combing the area where the jet might have gone down.
An EgyptAir official said the search was focused on an area of sea north of the Egyptian coast, without providing a precise location.
The flight from Paris Charles de Gaulle airport to Cairo normally takes just over four hours and the plane was scheduled to arrive at 3:05 am.
French President Francois Hollande called his Egyptian counterpart Abdel Fattah al-Sisi and the leaders agreed to "cooperate closely" to establish what happened to the plane.
Hollande also set up a crisis meeting of top ministers, including Valls, the foreign, defence and interior ministers, according to sources close to his office.
The passengers also included two Iraqis and one citizen from each of Algeria, Belgium, Chad, Portugal, Saudi Arabia and Sudan, as well as 30 Egyptians, the airline said.
They included a boy and two babies. Seven crew members and three security men were also on board.
EgyptAir said the plane had been manufactured in 2003. EgyptAir hit the headlines in March when a flight from the Egyptian coastal city of Alexandria to Cairo was hijacked and forced to divert to Cyprus, where the "unstable" hijacker demanded to see his ex-wife.
He had claimed he was wearing an explosive vest, which turned out to be fake, and handed himself in within hours after freeing the passengers and crew.
In October, the Islamic State jihadist group claimed responsibility for bombing a Russian airliner flying home holidaymakers from the Egyptian resort of Sharm El-Sheikh, killing all 224 people on board.
The group said it had smuggled a bomb concealed in a soda can on board the plane at Sharm El-Sheikh airport.
The disappearance of the jet on Thursday comes more than two years after the start of one of the most enduring mysteries in aviation history.
Malaysia Airlines Flight MH370 vanished on March 8, 2014 en route from Kuala Lumpur to Beijing with 239 passengers and crew on board, mostly Chinese and Malaysians.
Authorities believe the Boeing 777 detoured to the remote southern Indian Ocean and then plunged into the water.