The police and army have been the main targets of a campaign of bombings and shootings since the military deposed president Mohamed Mursi of the Muslim Brotherhood last July.
The Interior Ministry said militants had opened fire on security forces as they arrived at their hideout in Borg El Arab, some 45 km (28 miles) south-west of Alexandria during an operation to "detain a number of terrorist elements".
The police officer killed in the raid was named as First Lieutenant Ahmed Saad and the dead militant as Hassan Abdel Aal, a 25-year old from the Nile Delta province of Dakahlia. A second militant was arrested, it said.
The security forces seized weapons including an explosive belt and two automatic weapons.