The vehicle was targeted near a school in the North Sinai provincial capital of El-Arish, it said in a statement, in the second such attack in recent days.
There was no immediate claim of responsibility but the region is a stronghold of the Islamic State (IS) jihadist group.
IS claimed a roadside bombing that killed a colonel and three soldiers on the outskirts of El-Arish on Wednesday.
Jihadists have regularly attacked security forces in the peninsula since the army ousted Islamist president Mohamed Mursi in July 2013.
They say their attacks are in retaliation for a government crackdown targeting Mursi supporters that has left hundreds dead and thousands imprisoned.
The authorities say hundreds of policemen and soldiers have been killed in attacks, mainly in North Sinai, since 2013.
Egypt's branch of IS also said it planted a bomb that caused the crash of a Russian airliner in the Sinai in October, killing all 224 people on board.