Seven people, including three passengers, are being held hostage aboard the EgyptAir plane after it diverted to Larnaca airport on the Mediterranean island during a domestic flight from Alexandria to Cairo.
An Irish national are thought to have been aboard, though it is not known if they are among those still being held.
The hijacker has been named by Cypriot government officials as Seif Eldin Mustafa, whose nationality has not been confirmed.
Egypt's civil aviation minister said the hijacker had not issued any "concrete" demands and that it is not yet clear whether the hijacker's claims that he had a suicide vest are true, but they were treating it as a "real threat".
Egypt's civil aviation minister told reporters: "There are seven people still inside the plane. The captain and his aide, one woman stewardess, one security officer and three passengers. I can't give you any more than this. I can't talk about the nationalities at this stage.
There are conflicting reports over his motive, with some saying the incident is related to his ex-wife and that she is now helping negotiations and others reporting that he is asking for the release of political prisoners in Egypt.
The man was initially named by Egyptian authorities as university professor Dr Ibrahim Samaha, but a passenger by that name denied any responsibility for the incident.
According to the BBC's Victoria Derbyshire programme, he said: "I was not the hijacker, I was simply a passenger on that plane and I was released alongside other passengers and had absolutely nothing to do with hijacking the plane.
"We did not know what was going on. We got on board the plane and we were surprised that the crew took all our passports, which is unusual for a domestic flight.
"After a while we realised the altitude was getting higher, then we knew we were heading to Cyprus. At first the crew told us there was a problem with the plane and only later did we know it was hijacked."
The airline said the plane, flight number MS181, was carrying 56 passengers and seven crew, as well as a security officer.
Among them were 26 foreigners, including eight Americans, four Britons, four Dutch, two Belgians, an Italian, a French national, two Greeks and one Syrian, the director of the Alexandria airport said.
State media in Cyprus is reporting that the hijacker is also seeking the release of prisoners in Egypt.
An EGYPTAIR official declared that 3 passengers, the pilot, co-pilot and 3 cabin crew members in addition to the hijacker are still onboard.— EGYPTAIR (@EGYPTAIR) March 29, 2016
There are reported to be three foreigners and four crew members left on the hijacked plane, along with the hijacker.
It is not known at this stage whether a reported Irish citizen is one of those still on board, or was released earlier when almost all passengers were allowed to leave the aircraft.
Local media in Cyprus have said the EgyptAir hijacker has handed over a letter saying he wants to live in Cyprus with his ex-wife.
Four foreigners and the flight crew remain on board EgyptAir flight MS181 which was forced to land in Cyprus by a hijacker who has claimed to be wearing a suicide belt.
There are unconfirmed reports that one Irish person is among passengers caught up in the plane hijacking in Cyprus.
The Department of Foreign Affairs said it could not confirm that an Irish person was on board the plane, but said it was aware of the situation and monitoring it closely.
There were about 81 passengers in total, including Egyptians, about 10 Americans and a small number of Britons. There are an additional seven crew members on board.
The majority of passengers have now been released from the Airbus plane. It was not immediately known whether the Irish person reported to have been on board was among those released.
Larnaca airport has been closed.
The hijacker has been named as 27-year-old Ibrahim Samaha. Al Jazeera report he is an asylum seeker who has requested a translator and political asylum. Some reports say he is an Egyptian national, but this has not been confirmed.
Cypriot government officials said that after the plane, an Airbus A320, landed at Larnaca airport this morning, the hijacker por hijackers demanded that police vehicles move away from the aircraft.
All passengers have now been released from a hijacked Egyptair plane in Cyprus, excepting four foreigners and a number of crew members, the airline has said.
Local media is reporting that about 20 passengers have been released from a hijacked plane in the Cyprus airport of Larnaca. Those released are understood to be Egyptian-national women and children.
About 45 passengers and seven crew members remain on the plane.
Local media have also reported the hijacker is requesting political asylum. This has not yet been confirmed, and there is a conflicting report that no demands at all have yet been made.
The hijacker of a passenger plane that has landed in Egypt is reported to have explosives strapped to his body.
A passenger has hijacked a plane which has landed at the Cyrpus airport of Larnaca, and there is reportedly a bomb on board.
The Egyptair passenger plane travelling from Egypt is understood to have 81 people on board, with an additional seven crew members.
Its flight route had been between the Egyptian cities of Alexandria to Cairo.
Our flight MS181 is officially hijacked. we'll publish an official statement now. #Egyptair— EGYPTAIR (@EGYPTAIR) March 29, 2016
It is thought one man is armed on the plane, and the Associated Press has reported a bomb is thought to also be on board.
The plane made an emergency landing at about 6.45am Irish time.
The hijacker has as yet not made any demands.