French President Francois Hollande said in a televised address that the plane had crashed early on Thursday.
The plane made "sudden swerves" mid-air and plunged before dropping off radars in the southern Mediterranean, Greece's defence minister said.
"At 3:39am the course of the aircraft was south and south-east of Kassos and Karpathos [islands] ... immediately after it entered Cairo FIR and made swerves and a descent I describe; 90 degrees left and then 360 degrees to the right," Defence Minister Panos Kammenos told a news conference.
Greek authorities mounted a search in the area south of the island of Karpathos without result so far, he said.
However, Egypt's civil aviation ministry said in a statement it was too early to confirm if the passenger plane had crashed.
According to EgyptAir, the plane took off from Paris' Charles De Gaulle Airport shortly after 11pm local time.
Greece is deploying military aircraft and a frigate to an area in the southern Mediterranean its defence ministry said.
The search for the missing EgyptAir plane was taking place at sea, about 130 nautical miles southeast of the island of Karpathos, the Greek defence ministry told Reuters news agency.
"One C-130 aircraft and an early-warning EMB-145H plane are already operating in the area. Another C-130 plane is on standby at Kasteli airport on the [southern Greek] island of Crete," Greece's military command said.