The airline says Flight 804 which left Paris on its was to Cairo vanished from radar early Thursday morning, shortly after entering Egyptian airspace.
Egyptian armed forces are searching for the plane.
The plane disappeared from radar at 2:45 a.m. local time while flying at 37,000 feet, EgyptAir says.
There reportedly was no distress call from the plane.
The airline has updated the number of people on board — saying there are a total of 66 people: 56 passengers — including one child and two infants — and 10 crew aboard the Airbus A320.
Earlier, it said 69 people were on board.
According to a statement out of Paris, French President Francois Hollande told Egypt's President Abdel-Fattah el-Sissi that France would help to determine the circumstances involving the plane's disappearance.
A spokesman for Airbus told reporters that the company is aware of the disappearance but doesn't have any official information on the incident.
In March, an EgyptAir flight was hijacked and made to fly to Cyprus by a man who was later described as "psychologically unstable." He remains in custody in Cyprus.
About Thursday's missing plane, The Associated Press reports:
The incident renewed security concerns months after a Russian passenger plane was blown out of the sky over the Sinai Peninsula. The Russian plane crashed in Sinai on Oct. 31, killing all 224 people on board. Moscow said it was brought down by an explosive device, and a local branch of the extremist Islamic State group has claimed responsibility for planting it.