"The military received an SOS message from the plane emergency devices," the ministry said in a statement late on Thursday, the Tass news agency reported.
It further said the flight had disappeared from radars two minutes after leaving Greek airspace, adding that passengers on board included 30 Egyptians, 15 French and one Briton.
Later, Greek authorities said the captain of a merchant ship had reported a "flame in the sky" some 130 nautical miles south of the Karpathos island.
Egyptian Prime Minister Sherif Ismail said the search was underway to find the plane and it was too early to rule out any explanation for the incident, including terrorism.
"We cannot exclude anything at this time or confirm anything. All the search operations must be concluded so we can know the cause," he said.
According to the latest reports, there were 56 passengers and 10 crew members on board. Earlier reports had suggested that 59 passengers were aboard but later the figure was revised by the country's aviation ministry.
The plane was expected to land in the Egyptian capital at 3.05 a.m. local time.
In March, an EgyptAir plane flying from Alexandria to Cairo was hijacked and forced to land in Cyprus by a man with what authorities said was a fake suicide belt. He was arrested after giving himself up.
EgyptAir has a fleet of 57 Airbus and Boeing jets, including 15 of the Airbus A320 family of aircraft, according to airfleets.com.