Army forces surrounded the home of a leading figure of the Sinai-based militant group Ansar Bayt al-Maqdis in the town of Sheikh Zuweid before shooting him dead on Saturday, the army spokesman said.
Forces called on the leading militant to turn himself in, said spokesman Mohamed Samir in a statement. The militant meanwhile initiated an exchange of fire with the army forces, threatening to detonate himself with an explosive belt.
Militants have stepped up attacks targeting security forces in Egypt, particularly in the Sinai peninsula, since the ouster of Islamist President Mohamed Mursi in July 2013 after mass protests against his rule.
Ansar Bayt al-Maqdis, which changed its name to Sinai Province after pledging allegiance to Islamic State fighters last November, claims responsibility for the majority of the attacks in the peninsula.