The bombing took place near El-Arish, regional capital of North Sinai where attacks on security forces have mounted since the army's ouster in July of Islamist President Mohamed Morsi.
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A parked car blew up as the military convoy passed, the security official said.
Wednesday's bombing was the deadliest since an August 19 ambush by gunmen on a convoy of security forces that killed 25 police officers in the town of Rafah in North Sinai.
That attack was the bloodiest in the Sinai Peninsula in several years.
Dozens of soldiers and police officers have been killed in near daily attacks in Sinai, especially since Morsi's July 3 ouster by the army.
Egypt's army has poured troops and armor into the restive peninsula to crush militant activity.
Tahrir unrest
At least one person was killed when Egyptian riot police stormed Cairo's Tahrir Square late Tuesday to disperse stone-throwing protesters, a health ministry official said.
Police backed by armored vehicles fired tear gas and shots after clashes in the square to scatter protesters who had gathered to mark the anniversary of deadly 2011 demonstrations.
One man was killed when he was struck by birdshot during the clashes, head of emergency services Ahmed al-Ansary told AFP. It was not immediately clear if he was a protester.
The crowds were marking the anniversary of 2011 protests against the military, which took power between President Hosni Mubarak's overthrow and his now deposed successor Mohamed Morsi's election in June 2012.
Egypt's security forces are also engaged in a sweeping crackdown on Islamist supporters of Morsi in other parts of the country.
The crackdown has resulted in more than 1,000 people being killed and more than 2,000 arrested nationwide since mid-August.
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