"The members of the terrorist cell were monitored when they were moving in a car, ready to carry out terrorist attacks. When the militants acknowledged they had been surrounded, they opened intense fire on the military, they were given a response," the ministry said in a statement quoted by the Extra News TV broadcaster, adding that all members of the group were eliminated during the shootout.
Three policemen were injured in the operation, the ministry added.
The ministry noted that the operation was launched after the National Security Department received information that several members of a terrorist group in the Jelban area in northern Sinai were planning a series of attacks on the armed forces and the police.
The Egyptian authorities have for years been engaged in anti-terror activities on the Sinai Peninsula, where militants have repeatedly staged deadly attacks. In 2014, a state of emergency was declared on the peninsula after militants attacked Egyptian security officers in the area.