"From the beginning it was determined that this was not a case of terrorism," Foreign Minister Ioannis Kasoulides said, adding the man was "psychologically unstable".
Egypt identified the man as 58-year-old Seif al-Din Mohamed Mostafa.
Kasoulides said the man demanded to deliver a letter to his Cypriot ex-wife, with whom he was said to have children.
She was brought to the airport and spoke to the man, the minister said, without elaborating.
He also delivered a rambling letter in Arabic with demands, including to meet with a European Union representative and for the release of women prisoners in Egypt.
"There was no logical consistency for the demands to be taken seriously," Kasoulides said.
Asked about the hijacker's demands to see his wife, Cyprus President Nicos Anastasiades laughed and said: "Always there is a woman."
- Fake explosives -
The EgyptAir plane landed in Larnaca at 8:50 am (0550 GMT), after the hijacker had contacted the control tower 20 minutes earlier to demand the diversion.
Egyptian civil aviation officials said there were 21 foreigners among the passengers, and that the hijacker had demanded the plane land in either Turkey or Cyprus.
They included eight Americans, four Dutch citizens and four Britons, the Egyptian authorities said.
Two French nationals were also on the plane, according to a French diplomatic source.
Officials said that seven people, including several passengers, had remained on board until shortly before the man surrendered.
The hijacker emerged from the aircraft, walked across the tarmac and raised his hands to two waiting counter-terrorism officers. They laid him on the ground and searched him before taking him away.
In a tweet at 2:43 pm, Cypriot government spokesman Nicos Christodoulides confirmed "the hijacker has just been arrested" and that all crew and passengers were safe.
After sending sniffer dogs onto the plane, police said no bombs had been found.
Kasoulides said the man had threatened to blow himself up if the plane was not refuelled and allowed to depart for Istanbul.
"We examined the alleged explosives that were found on him. They were not explosives but phone covers made up to give the impression they were explosives," he said.
Police said there were no immediate indications anyone had been working with the hijacker.
- Airport reopens -
Authorities closed the airport -- Cyprus's main entry point for tourists -- and nearby beaches and diverted incoming flights to Paphos in the island's west.
Larnaca airport later said it had reopened and that flights had resumed.
Egypt sent a plane that flew home passengers who were aboard the hijacked jet.
It also released photographs it said were of the hijacker being searched by airport security before boarding the plane.
Concerns were raised about security at Egyptian airports after a Russian airliner was downed on October 31 over Sinai Peninsula, killing all 224 people on board.
The Islamic State group claimed to have smuggled a bomb on board.
Larnaca is no stranger to hostage crises. Several hijacked planes were diverted to the airport in the past few decades.
In August 1996, a Sudan Airways Airbus A-310 was hijacked by seven Iraqis between Khartoum and Amman with 199 people on board. After a stopover in Larnaca it flew on to London's Stansted airport, where the hijackers gave themselves up.
In 1988, a Kuwait Airways flight hijacked en route from Bangkok to Kuwait was diverted to Iran and later to Larnaca, where hijackers killed two Kuwaiti passengers and dumped their bodies on the tarmac.
In February 1978, Egyptian commandos stormed a hijacked Cyprus Airways DC-8 at Larnaca, where 15 passengers were being held hostage. Some 15 Egyptian soldiers were killed and 15 wounded in a firefight with Cypriot forces. All the hostages were freed and the hijackers arrested.