The Airbus A320 went missing at 02:30 Cairo time (00:30 GMT), soon after leaving Greek airspace.
There were 56 passengers – including three children – seven crew members and three security personnel on board Flight MS804, EgyptAir said.
Airbus confirmed “the loss” of the 13-year-old plane.
A major search and rescue operation is under way involving the Greek and Egyptian armed forces. France has offered to send boats and planes to help in the effort.
Both French and Egyptian officials have refused to be drawn on what has happened to the plane, which had 30 Egyptians, 15 French citizens and one Briton among those on board.
Although there is no evidence yet to indicate a malicious attack, the spectre of terrorism inevitably looms over this latest aviation tragedy, says the BBC’s security correspondent Frank Gardner.
R.I.P.