EgyptAir Flight MS181 was taken over after a passenger claimed to be wearing a suicide explosive belt.
Reports say the lone hijacker wants to talk to his estranged wife in Cyprus, and the Cypriot president has said the hijack is not a terrorist incident.
Egypt’s civil aviation minister said seven people remained on board the jet.
Sherif Fathy identified them as the pilot, the co-pilot, a female stewardess, a security officer and three passengers whose nationalities he refused to divulge.
He said negotiations with the hijacker – who had made no specific demands – were continuing, and that it was unclear whether the hijacker had taken explosives on board or whether he was bluffing.
An aircraft was being sent to Larnaca to pick up the passengers who had been released, Mr Fathy added.
Cypriot President Nicos Anastasiades said: “We are doing our utmost in order for everyone to be released and safe.”
In response to a reporter’s question about whether the hijacker was motivated by romance, he laughed and said: “Always there is a woman involved.
Negotiations began and then people were seen emerging from the plane
EgyptAir said the Airbus A320 was carrying 56 passengers from Alexandria to Cairo, along with six crew and a security official. It had earlier said 81 passengers were on board.
A senior Alexandria airport official said those on board the flight when it took off included eight Americans, four Britons, four Dutch, two Belgians, one Italian and 30 Egyptians.
“The pilot said that a passenger told him he had an explosives vest and forced the plane to land in Larnaca,” the Egyptian civil aviation ministry said in a statement.
Larnaca airport, on the south coast of Cyprus, has been closed and scheduled flights diverted elsewhere.