According to Egypt's Aviation Ministry, the passengers included 30 Egyptians, 15 French and one Briton.
The Airbus A320 was flying at 37,000 feet (11,300 meters) when it went missing over the eastern Mediterranean, 10 miles into the Egyptian airspace.
An official said the plane lost contact with radar at 02:45 Cairo time (00:45 GMT).
The airline said the flight sent a distress message before vanishing from radar screens that was detected by the military.
The message was received at 0226 GMT, less than 10 minutes before the flight disappeared, AFP quoted it as saying.
Greek Defense Ministry said it has deployed frigate, military aircraft to southern Mediterranean in an effort to locate the plane.
Greek authorities were also investigating an account from the captain of a merchant ship who reported a "flame in the sky" some 130 nautical miles south of the Karpathos island.
The country's civil aviation chief said the flight disappeared from radars two minutes after leaving Greek airspace.
French Prime Minister Manuel Valls said nothing can be ruled out regarding the possible cause of the crash.
An Airbus A321 operated by Russia's Metrojet crashed in Egypt's Sinai peninsula on October 31, 2015, killing all 224 people on board.
The plane was likely brought down by a bomb, and the Daesh group said it had smuggled an explosive on board.
In March, an EgyptAir plane flying from Alexandria to Cairo was hijacked and forced to land in Cyprus by an "unstable" man who demanded to see his ex-wife.
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