A statement said the crash in the Mediterranean coastal town of Marsa Matrouh was due to a “technical fault”. It did not make clear whether all the dead and injured were aboard the aircraft.
The Egyptian army and air force were conducting a joint operation against militants in the border area and destroyed four of their vehicles, a military spokesman said.
Egypt is facing an increasingly brazen insurgency based in the Sinai region that has killed hundreds of police and soldiers since the army ousted Islamist President Mohamed Mursi after mass protests against his rule in 2013.
Security officials say militants operating from Libya to the west of Egypt have been trying to forge ties with Islamists in the Sinai on the east side of the country.
Sinai Province, Egypt’s most active jihadist group, swore allegiance last year to Islamic State, the ultra-radical Sunni militant group that has seized expanses of Iraq and Syria, drawing U.S.-led air strikes.
Egyptian jets bombed Islamic State targets in Libya in February, a day after the group there released a video showing the beheading of 21 Egyptian Christians, drawing Cairo directly into factional conflict across its border.