EgyptAir flight MS804 from Paris to Cairo has disappeared from radar, the Egyptian flag-carrier has confirmed.
French President Francois Hollande said the plane likely crashed on route to the Egyptian capital.
Greece defence minister Panos Kammenos added it appeared the plane made two sharp turns before plunging into the Mediterranean Sea.
He explained the plane “turned 90 degrees left and a 360-degree turn to the right” before it dropped more than 20,000 feet and disappeared from radar screens.
Some 56 passengers, seven crew members and three security personnel were on board the Airbus A320 when it disappeared at 00:45GMT.
Of the people on board, 30 are believed to be Egyptians, while there are also 15 French and ten other nationalities, including one Briton.
The plane was flying at 37,000ft when it went missing over the eastern Mediterranean, ten miles from Egyptian airspace and half an hour from landing.
EgyptAir said search and rescue teams have been deployed.
The aircraft left Paris’ Charles de Gaulle airport at 21:09 GMT on Wednesday.
It was scheduled to arrive in the Egyptian capital soon after 01:00 GMT on Thursday.
Amid fears that the plane has crashed into the Mediterranean, Greek authorities have joined Egyptian armed forces in the search operation.
French prime minister Manuel Valls, speaking to RTL radio earlier, said: “At this stage, no theory can be ruled out regarding the causes of the disappearance.”
Last October, a Russian passenger plane flying from Sharm el-Sheikh crashed over the Sinai peninsula killing all 224 people on board.
Officials in Moscow and Egypt later said the aircraft was brought down by an explosive device.
Islamic State militants said they had bombed the plane.
In a statement plane manufacturer Airbus said: “The aircraft involved, registered under SU-GCC was MSN 2088, was delivered to EgyptAir from the production line in November 2003.
“The aircraft had accumulated approximately 48,000 flight hours.”
In line with ICAO annex 13, Airbus said is stood-by ready to provide full technical assistance to the French Investigation Agency - BEA - and to the authorities in charge of the investigation.
The first A320 entered service in March 1988.
At the end of April 2016 over 6,700 A320 Family aircraft were in operation worldwide.
To date, the entire fleet has accumulated nearly 180 million flight hours in over 98 million flights.
The incident is the latest setback for Egyptian tourism.
Kinda Chebib, senior analyst, Euromonitor International argued: “If we analyse tourist’s performance prior the political unrest in 2011 and recurring attacks by jihadist militants (such as Sinai), arrivals from key markets plummeted in 2011 and started gradually to recover until 2015.
“But those never achieved the performance from prior the events.
Egypt can restore its image when it comes to specific, location-limited events, but when we speak of such big proportion of security breach, and when international terrorists groups are involved in the frame of a larger geopolitical issue, there is no doubt that it will take a while for the Egyptian tourism and economy to get back on its feet.
“We can therefor speak of an impact on the mid- to long-term.
Despite the decline of 18 per cent in 2012-2013, 2014 was a good year for Egyptian tourism, inbound flows rose by eight per cent to reach 10.2 million arrivals, up from 9.5 million in 2013.
The UK is the second biggest source market for Egypt, with one million arrivals in terms on trips to the country in 2014, after Russia, which recorded in 2014 nearly three million arrivals.
Chebib added: “Travellers are likely to remain very hesitant to travel to this part of the Middle East and will opt for destinations like the Gulf countries or in North Africa they are likely to choose Morocco, contrasting with more vulnerable destinations like Tunisia and Egypt.
“Although Egypt is known for quickly bouncing back from different crises, we believe that the recent events will slow down the ambitions of the local government to achieve the target of 20 million foreign tourist arrivals by 2020.”