An EgyptAir flight from Paris to Cairo made two sharp turns before plunging into the Mediterranean Sea, Greece's defence minister says.
Panos Kammenos said the Airbus A320 had "turned 90 degrees left and a 360-degree turn to the right" and dropped more than 6,700m (20,000ft) before disappearing from radar.
Sixty-six people were on board, most of them from Egypt or France.
A major search is under way in seas south of the Greek island of Karpathos.
Greek and Egyptian armed forces are involved in the effort, and France has offered to send boats and planes.
Egypt's Civil Aviation Minister Sherif Fathi told a news conference it was too early to rule out either terrorism or a technical failure as the reason behind the plane's disappearance.
He said search efforts were concentrating on an area of the Mediterranean near the Greek island of Karpathos, but no wreckage had yet been found.
Of those on board, 56 were passengers, seven were crew members and three were security personnel. A Briton was among those on board.
Flight MS804 left Charles de Gaulle airport in Paris 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.
EgyptAir said the plane had been flying at 11,300m (37,000ft) when it disappeared from radar shortly after entering Egyptian airspace.
Greek aviation officials say air traffic controllers spoke to the pilot when he entered Greek airspace and everything appeared normal.
They tried to contact him again at 02:27 Cairo time, as the plane was set to enter Egyptian airspace, but "despite repeated calls, the aircraft did not respond". Two minutes later it vanished from radar.
French President Francois Hollande said he was keeping an open mind about the cause: "We will draw conclusions when we have the truth about what happened.
"Whether it was an accident, or whether it was - and it's something that is on our minds - terrorism."
He has spoken to his Egyptian counterpart and both leaders have been holding emergency meetings with their top officials, according to reports from both countries.
