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 the Swiss city at 6 a.m. (0500 GMT) and the hijacker was arrested. Police spokesman Jean-Philippe Brandt told The Associated Press that "the situation is under control" and nobody on the flight was injured.
Further details of the incident were to be released at a news conference in Geneva at 9 a.m. (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. The officials spoke on condition of anonymity because they are not authorized to brief the media.
Geneva airport said departures would resume at 8.15 a.m. (0715 GMT) and arrivals at 8.45 a.m. (0745 GMT).
Frank Jordans in Berlin and Maamoun Youssef in Cairo contributed to this report.