The EgyptAir plane was taken over by at least one armed man while flying from Alexandria on Egypt’s Mediterranean coast to the capital Cairo, the country’s civil aviation authority said.
Reports have suggested that eight Britons and 10 American citizens were on board.
The plane landed at Larnaca airport where negotiations have led to the release of all the passengers, except for the crew and four foreigners, the airline said.
In a statement on Twitter, EgyptAir said there was a threat from a passenger with an explosive belt.
The Airbus was carrying 81 passengers, as well as seven crew.
Cypriot government officials said that after the plane, an Airbus A320, landed at Larnaca airport on Tuesday morning hijackers demanded that police vehicles move away from the aircraft.
One official said it “seems like there’s more than one hijacker” on the plane.
The plane landed at Larnaca airport at around 8.50am, police in Cyprus said.
It is not clear how many hijackers are aboard the plane but EgyptAir said the captain, Omar Jamal, was alerted to the presence of a passenger who was wearing an explosive belt.
Footage from the airport shows the plane on a runway and passengers leaving the aircraft before getting on to waiting buses with their luggage.
Journalist Vanita Zannetu who is at the airport told BBC 5 Live she could see passengers disembarking from the plane.
“I can see now some passengers coming down from the aeroplane, going to the bus, most probably they are going to go to the building of Larnaca airport. So this is what we know until now.”
She added: “We don’t know whether the passengers that are coming down now are Greek Cypriots or whether they are other nationalities. We don’t know yet. But as I can see there are quite a lot of them coming out.”
She said the passengers appeared to be adults and were holding their personal luggage.
The Foreign and Commonwealth Office could not confirm whether any Britons were among the passengers, saying: “We are in contact with the Cypriot and Egyptian authorities after a hijacked plane landed in Cyprus.”
Ireland’s department of foreign affairs said it is liaising with consular staff in Egypt but could not confirm if an Irish citizen was on board the plane.
A spokeswoman said: “We are in contact with consular staff. We are aware of the rumours but we are not in a position to confirm if an Irish citizen is or is not on the plane at this stage.”
A motive for the hijacking is unclear but the incident will raise questions over security at Egyptian airports, coming just five months after 224 people were killed when a Russian aircraft crashed over Egypt’s Sinai Peninsula minutes after it took off from the Red Sea resort of Sharm el-Sheikh.
Russia later said an explosive device brought down the aircraft, and the extremist Islamic State group (IS) said it was responsible.
Cyprus is a popular tourist destination for British holidaymakers, with around a million visiting every year.
Flights are being diverted away from Larnaca airport as a result of the hijacking, and the Foreign Office urged anyone travelling to the country to contact their airline or travel company.