Two Egyptian soldiers were also killed late on Saturday when an improvised explosive device detonated in a road in the North Sinai town of Sheikh Zuweid, near the border of the Gaza Strip.
Radical Islamists in the rugged desert region adjoining Israel, who expanded into a security vacuum left by the overthrow of Hosni Mubarak in 2011, have been staging almost daily assaults on security forces and other targets.
Dozens of tanks and armoured vehicles backed by attack helicopters were used earlier in Saturday's operation near Sheikh Zuweid, which is only a few miles from the Palestinian Gaza Strip, security sources said.
The army said nine militants had been arrested.
Since the army toppled Islamist President Mohamed Mursi on July 3, and especially since security forces killed hundreds of Islamists when they smashed protest camps in Cairo on August. 14, there have been online calls from Islamist radicals for wider attacks on the state.
Egyptian memories of an Islamist insurgency in the 1990s were revived on Thursday when a suicide bomber blew up a car bomb next to the interior minister's convoy in Cairo.