EgyptAir says it received a distress signal before the plane disappeared from radar.
There were 56 passengers – including three children – seven crew members and three security personnel on board Flight MS804, the airline said.
The airline said the passengers included 30 Egyptians, 15 French citizens, one Briton, two Iraqis, as well as people from Canada, Belgium, Kuwait, Saudi Arabia, Algeria, Sudan, Chad and Portugal.
Flight MS804 left Paris’ Charles de Gaulle airport at 23:09 local time on Wednesday (21:09 GMT) and was scheduled to arrive in the Egyptian capital soon after 03:00 local time on Thursday.
It was flying at 37,000ft (11,300m) over the eastern Mediterranean when contact was lost, at 02:45 Cairo time (00:45 GMT).
The Greek authorities joined Egyptian armed forces in the search operation.
Earlier an airport official, quoted by Egypt’s state-run newspaper al-Ahram, said the last contact with the plane had been 10 minutes before it disappeared – and no distress signal had been sent.
But EgyptAir tweeted (in Arabic) that a distress signal was sent from the plane’s emergency devices.
Flightradar24 listed details of the plane’s journey on Wednesday which showed it had flown from Asmara, in Eritrea, to Cairo, then on to Tunis, in Tunisia, before heading, via Cairo, to Paris.
Egyptian Prime Minister Sherif Ismail has arrived at the airport in Cairo, along with the families of those on board, state-run Nile News TV reports.
Aviation analyst Alex Macheras told the BBC that Airbus A320s were regularly used for short-haul budget flights and had “an amazing safety record”.
In March, an EgyptAir plane was hijacked and diverted to Cyprus. The attacker later surrendered and all hostages were released.
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.
If anyone is concerned about relatives or friends following the disappearance of the flight, they can call this free number provided by EgyptAir: +202 259 89320.