Security officials said the attack was in response to early morning police raids on the homes of suspected militants that led to the arrests, backing away from an earlier report that the militants had taken children hostage to be used as human shields.
Col. Ahmed Mohammed Ali, the military spokesman, said the clashes began shortly after the raids, when militants fired rocket-propelled grenades and automatic rifles on the security building and troops. He said seven soldiers were wounded, and one later died of his wounds.
Security officials said at one point, fighters briefly used a school wall as cover as children were arriving. The military spokesman said the wounded included an elderly woman and a 10-year old child.
The dawn raids by police backed by the military focused on a number of homes in Sheik Zuweyid, a desert village about 30 kilometers (18 miles) from northern Sinai's main city of el-Arish. Security officials said four men suspected of belonging to extremist militant groups were arrested.
But Ali later said the military operation, in which the air force was involved, resulted in the arrest of 10 suspected militants in a village east of Sheik Zuweyid.
The security officials spoke on condition of anonymity according to police and military regulations.
The rugged Sinai peninsula of barren deserts and daunting mountains, with a population of around 400,000, has long been a volatile corner of Egypt where militants, smugglers, and restive tribes find sanctuary.
Since last year's uprising that ousted longtime authoritarian President Hosni Mubarak from power, Sinai has spiraled out of control. Across Egypt, police and internal security forces fell apart during the uprising. They have returned to the streets in some areas, but in Sinai, particularly in the north, their presence remains weak.
In a sign of how emboldened the militants have become, during Sunday's fighting a group chased down 13 armored personnel carriers that had conducted the raids, firing at them and at a helicopter involved in the security sweep. Ali said a camera in the aircraft was damaged.
Later the same morning, militants in Land Cruisers fired rocket-propelled grenades and bullets at northern Sinai's main security headquarters in el-Arish, two police stations in the area and a checkpoint. No one was wounded in those attacks.
Such attacks are common in the Sinai.
On Friday, in the midst of protests against an anti-Islam film produced in the United States, militants waving black banners and shouting "God is great!" stormed an international peacekeepers' base in northern Sinai and attacked troops, wounding two Colombians. They stole some weapons and radio equipment, officials said.
The base near the border with Gaza and Israel houses some 1,500 members of the force, including U.S. troops.