After the minister emerged unscathed, the cabinet vowed it "will strike with an iron hand (against) those who threaten national security until stability returns" across the country.
"The cabinet insists that this criminal act will not prevent the government from confronting terrorism with force and determination," the cabinet said.
Preliminary reports suggested a car bomb or a timed device may have targeted the minister as his convoy left for work in the capital's Nasr City district.
Six security officers and a child were among the injured, according to Egypt's Ambulance Authority.
Hours after the attack, Ibrahim appeared on state TV to condemn the "cowardly assassination attempt", saying his convoy was targeted by a bomb that wounded "many guards" with some sustaining severe injuries, including leg amputations.
Ibrahim said he had warned of such violence after the August 14 crackdown on Islamists who had set up camps in Cairo to protest the military's removal of Morsi on July 3.
While the exact source of the bomb is not yet known, the Egyptian TV said the bomb was dropped from the roof top of a nearby building. The building has been pinpointed and investigations are underway, it added.
The capital's Nasr City area has been the stronghold of a major protest camp by loyalists of Egypt's toppled Islamist president Mohammed Morsi.
The bombing, which comes as security forces intensified clampdown on Morsi supporters, has sparked fears of a resurgence of the Islamist militant assaults that plagued Egypt in the 1990s.
"The bombing should be condemned irrespective of the perpetrators," the Anti-Coup Alliance said, citing one of its senior members.
Hundreds of Morsi supporters were killed and thousands injured in the deadly raid by police to clear protest camps in Cairo's Rabaa al-Adawiya and Nahda squares which led to days of bloody street violence pitting Islamist against security forces.
