Police Captain Ayman al-Desouky, who had gone missing near the town of Rafah on the border with the Gaza Strip on Sunday, was "killed by terrorist elements," it added.
His body was found with a bullet to the head after a joint search with police across the North Sinai towns of El-Arish, Sheikh Zuweid and Rafah, during which the "10 terrorists" were killed in a shootout.
It was not immediately clear who had killed the officer but jihadists based in the restive Sinai have claimed a string of killings of security force personnel.
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Egypt's deadliest militant group, Ansar Beit al-Maqdis (Partisans of Jerusalem) is based in the peninsula and pledged allegiance in November to the Islamic State group in Iraq and Syria.
Egypt's military has been battling an insurgency in the region ever since it overthrew Islamist president Mohamed Morsi in 2013.
The government declared a state of emergency in parts of North Sinai after an October 24 suicide attack near El-Arish killed 30 soldiers in the deadliest assault on security forces since Morsi's ouster.
Militant groups claim their attacks are in retaliation for a government crackdown targeting Morsi's supporters that has left hundreds dead and thousands jailed.