Seven civilians, including two young children, were killed when the bomb exploded at a security checkpoint in the Sinai Peninsula.
The military said the tank intercepted the vehicle at a checkpoint near the city of Arish, the capital of North Sinai province, and tried to contain the expected blast by running over the car.
Video footage showed the tank accelerate to meet the car as it raced towards the checkpoint.
It then ran the car over, which carried four gunmen.
The tank retreated as civilians ran for cover, at which point the car exploded and nearby civilians were caught in the blast.
An army spokesman said the attack could have killed 50-60 people had it reached its target.
“The explosion was large, carrying about 100kg of high explosives,” the statement said.
No group has claimed responsibility for the attack.
An insurgency in Egypt's Sinai region has gained pace since the army toppled President Mohamed Morsi of the Muslim Brotherhood, Egypt's oldest Islamist movement, following mass protests against his rule in mid-2013.
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