There were no immediate reports of the discovery of any debris but both Egypt and Greece said they had dispatched aircraft and naval vessels to the area on a search and rescue mission.
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.
The Islamic State jihadist group has been waging a deadly insurgency against Egyptian security forces and last October claimed the bombing of a Russian airliner flying home holidaymakers from the Egyptian resort of Sharm El-Sheikh, which killed all 224 people on board.
EgyptAir said contact was lost with the flight about 280 kilometres (175 miles) north of the Egyptian coast.
The Greek aviation source said the flight had disappeared from Greek radar at around 0029 GMT.
“It crashed around 130 nautical miles off the island of Karpathos,” the source told AFP, referring to an island northeast of Crete.
The official said the last communication with the pilot was three minutes before the plane disappeared, and that there had been no distress call.
EgyptAir Holding Company vice president Ahmed Adel also said there had been “no distress call” before it vanished.
EgyptAir had said military search and rescue had detected a “distress message,” but the army denied detecting any such message.
A tweet on the airline’s official account said Flight MS804 left Paris at 11:09 pm (2109 GMT), “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).
An airline statement said: “The cause of the airplane’s disappearance is not yet known.”
Egyptian Prime Minister Sharif Ismail told reporters “we can’t preclude or confirm anything yet,” when asked if the flight could have been attacked.
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 (0105 GMT).
France crisis meeting
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.
Last October, foreign governments issued travel warnings for Egypt and demanded review of security at its airports after the Islamic State group downed the Russian airliner with what it said was a bomb concealed in a soda can that had been smuggled into the hold.
The disappearance of the EgyptAir jet 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.