In a tweet the ministry says the hijacker, which it had earlier identified as Seif Eldin Mustafa, had been arrested.
Hours earlier, Egypt had said all but four crew and three passengers remained on board the plane, which had been forced to land at Larnaca airport in Cyprus.
State television had shown several people leaving the plane, including one exiting through a cockpit window.
Egypt's Civil Aviation Minister Sherif Fathy confirmed a passenger had approached the pilot claiming to have an explosives belt.
"The reality is we have a hijacker on board of a plane, we're not sure whether what he has is a true bomb or threat to the aircraft, but we are dealing with it as a real threat, because we cannot take any risk except dealing with it as a serious situation."
The Airbus 320 had been enroute from Alexandria to Cairo with 55 people on board.
There were conflicting reports on the hijacker's motives, with Cyprus' state broadcaster reporting he had asked for the release of female prisoners in Egypt.
Some media outlets reported it had been personal, a theory Cypriot President Nicos Anastasiades had seemed to confirm.
"We are doing our utmost in order for everyone to be released and safe, and to bring an end to this unprecedented...in any case it's not something which has to do with terrorism. You know what I mean? (laughs)"
