No group has claimed responsibility, but Al-Qaeda-linked Islamist militants in the largely lawless Sinai region have stepped up attacks on soldiers and police since the army toppled Islamist President Mohamed Morsy in July. The militants have on occasion extended their campaign into major cities.
Military spokesperson Ahmed Ali said in a statement the bombing was "a continuation of the wave of cowardly terrorist attacks," by groups he described as promoting strife.
Security personnel searching the area found another car bomb, which had not gone off, state media and security sources said. Heavy smoke could be seen rising from a building nearby.
The force of the blast caused part of the military intelligence building's outer wall to collapse.
Some security sources said the bomb was planted in a car belonging to a doctor who lived in a nearby building.
