The attack took place in Al-Arish, in the country's North Sinai province, tha Al-Ahram news agency reported, citing the local health ministry.
As the truck headed toward the camp's gate, guards shot at it, and the truck exploded.
The injured included 42 Egyptian soldiers and two civilians. The driver of the truck was also killed, Al-Ahram said.
No one has claimed responsibility for the attack.
North Sinai has been the site of dozens of recent deaths. In January, at least 26 people were reportedly killed and dozens more wounded, in a series of militant attacks on army and police positions in Egypt's volatile Sinai Peninsula.
The Egyptian army is battling an Islamist insurgency in North Sinai that has spiked since the 2013 ouster of Islamist President Mohamed Morsy.
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