The airline said one of its planes had been "forced to proceed to Geneva". Its website said the flight landed safely and "all passengers and crew are safe". It gave no further details.
Swiss police said the plane made an unscheduled landing in Geneva at 6am local time (0500 GMT) and the hijacker was arrested.
Police spokesman Jean-Philippe Brandt said that "the situation is under control" and nobody on the flight was injured.
Further details of the incident were due to be released at a news conference in Geneva at 9am (0800 GMT).
Cairo airport officials said the pilot of the plane, flight 702, informed the control tower at Abu Simbel in southern Egypt that his plane had been hijacked. The pilot did not ask to land in Egypt, and the plane headed for Libyan airspace, they said.
Geneva airport said departures would resume at 8.15am (0715 GMT) and arrivals at 8.45am (0745 GMT).
A Swiss official said the co-pilot took control of the aircraft while the pilot was in the toilet, and wanted to seek asylum in Switzerland.
Geneva airport chief executive Robert Deillon told reporters that the co-pilot - an Ethiopian man born in 1983 - locked himself in the cockpit after taking control.