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 03:15 local time on Thursday.
It was flying at 37,000ft (11,300m) over the eastern Mediterranean when contact was lost, at 02:30 Cairo time (00:30 GMT).
In what is thought to have been the last known contact with the plane, Greek air traffic controllers spoke to the pilot over the island of Kea, just south-east of Athens, and he "did not mention any problems", Kostas Litzerakis of Greece's civil aviation department told Reuters news agency.
A Greek aviation official told the AFP news agency that the plane crashed "around 130 nautical miles" off the southern Greek island of Karpathos, although this has not been confirmed.
Both the Greek and Egyptian armed forces are involved in the search for the plane. France says it is sending boats and planes to help in the operation.
EgyptAir flight MS804
people on board - 56 passengers, seven crew members and three security personnel
15 French citizens
1 from Britain, Canada, Belgium, Kuwait, Saudi Arabia, Algeria, Sudan, Chad and Portugal
There was some confusion over whether a distress signal was sent by the plane.
Egypt's state-run newspaper al-Ahram quoted an EgyptAir statement as saying the Egyptian army's rescue and search had received a distress call from the plane at 04:26 local time - which would be around two hours after the flight disappeared.
But the Egypt's military subsequently said that no such signal was received.
Spotlight falls on French security: Analysis by Hugh Schofield in Paris
If this turns out to be a terrorist attack, then eyes will turn first of all to Charles de Gaulle airport, from where Flight MS804 took off on Wednesday night. Could there have been a breach of security allowing a device to be smuggled on board?
Security at Charles de Gaulle, which was already tight, has been tightened even further since the Paris attacks in January 2015 and last November. There is the visible security, with soldiers on patrol, but more important is what is not seen - the monitoring of passengers and staff.
One weak point identified in recent years has been the large number of flight-side workers who come from high-immigrant areas of the Paris suburbs. Last year there was a security review of the 86,000 workers with authorisation to go flight-side. More than 60 had their authorisation withdrawn because of fears of Islamic radicalisation.
Of course, the investigation will also look at another possibility - that the device, if there was one, was smuggled on elsewhere.
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.
Families of those on board the flight have gathered at both Cairo airport and Paris' Charles de Gaulle to await news.
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.