A government source told AFP the hijacker had demanded to see a Cypriot woman, his estranged lover who lives on the island.
The EgyptAir plane landed at the airport in the southern coastal city of Larnaca at 8:50 am (1120 IST), after the hijacker had contacted the control tower 20 minutes earlier to demand the diversion.
Egyptian civil aviation said he had threatened to detonate an explosives belt on the Airbus A-320, which had been headed from the Mediterranean coastal city of Alexandria to Cairo.
EgyptAir had previously said that negotiations with the hijacker" had resulted in "the release of all the passengers, except the crew and four foreigners."
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An AFP correspondent later saw at least seven people descend from the aircraft, including some dressed in what appeared to be crew uniforms.
The plane had been carrying 21 foreigners including eight Americans, four Dutch citizens, four Britons and a French citizen, an Egyptian civil aviation ministry statement said.
"He had no gun or anything. We don't know yet whether his (explosives) belt is real but for the safety of passengers we are dealing with it as real," Fathy said.
Cyprus President Nicos Anastasiades told reporters the incident appeared to be motivated by personal reasons.
"The hijacking is not terrorism-related," he told a joint news conference with the visiting president of the European Parliament, Martin Schultz.
Asked about reports that the hijacker had demanded to see a Cypriot woman, Anastasiades said: "Always there is a woman."
Cyprus state radio had earlier reported that the man was demanding asylum and had asked for a translator.
A crisis team was deployed to the airport, the main entry point for tourists to the Mediterranean resort island.