Egypt's Civil Aviation minister on Tuesday said seven people remained on the plane after all others were released by the hijacker.
Aviation minister Sherif Fathy at a news conference in Cairo said three of those still on board were foreign passengers. The pilot and co-pilot, one flight attendant and an air marshal were also held, he added.
Initial reports said that the pilot of the plane was threatened by a passenger strapped with explosives, but Fathy said this has not been confirmed.
Cyprus President Nicos Anastasiades said the hijacker seemed to have a personal motive and that the incident was"not related to terrorism".
EgyptAir said that 81 people were on board, including a crew of seven. Passengers on EgyptAir flight 181 included 10 Americans, eight Britons and four Dutch people, security sources at Alexandria airport said.
The plane was an Airbus 320, Egypt's aviation ministry said. An official with flight-tracking website FlightRadar24 said the plane showed no immediate signs of distress. The flight between Alexandria and Cairo normally takes about 30 minutes.
The ministry said in a statement that pilot Omar al-Gammal had informed authorities that he was threatened by a passenger who possessed a suicide belt and forced him to land in Larnaca.
Cyprus foreign ministry identified the hijacker as Seif Eldin Mustafa and said it could not confirm the man was rigged with explosives. Egyptian state TV published a picture of the alleged hijacker, taken by one of the passengers
Cyprus state TV said that the hijacker wanted to contact his ex-wife, who lives in Larnaca.
Witnesses told Cyprus Mail newspaper that the he threw a letter on the apron of the airport in Larnaca, written in Arabic, asking that it be delivered to his ex-wife, who is Greek-Cypriot. She was reportedly on her way to the airport to participate in the negotiations. Other media outlets in Cyprus reported he first asked to be taken to Istanbul but that the pilot refused this demand.
CYBC said the airplane was parked at an apron at Larnaca airport. The hijacker asked police to back away from the aircraft, it said.
EgyptAir offered those concerned about their loved ones possibly being on a hijacked flight several telephone numbers to call for more information. Egypt's vital tourism industry was already reeling from the crash of a Russian passenger plane in the Sinai in late October.
President Abdel Fattah al-Sisi has said it was brought down by an attack. Islamic State of Iraq and the Levant (ISIL, also known as ISIS) has said it planted a bomb, killing all 224 people on board. Cyprus has seen little militant activity for decades, despite its proximity to the Middle East.
A botched attempt by Egyptian commandos to storm a hijacked airliner at Larnaca airport led to the disruption of diplomatic relations between Cyprus and Egypt in 1978.