Hours later, he appeared unharmed on state TV to denounce the attack as a “cowardly assassination bid”.
Security guards and a child were among the injured in the attack, which took place near his home in Nasr City.
No-one has yet claimed responsibility for the attack. Muslim Brotherhood leader Amr Darrag said the group “strongly condemned” what happened.
Mr Ibrahim heads the police force which has carried out a crackdown on Muslim Brotherhood protests in recent weeks.
Nasr City is a stronghold of the Islamist Muslim Brotherhood group.
‘Foiled assassination bid’
The explosion took place at about 10:30 local time (08:30 GMT) as Mr Ibrahim was being driven from his home to work.
The minister told state television that his convoy was targeted by a “large” explosive device that might have been detonated by remote control.
“It destroyed four of the vehicles of my protection team, with many shops in the area badly affected along with a vehicle of civilians and a small child who had a leg amputated,” he said.
“I have an officer with serious injuries and another officer with a leg amputation. There were many injuries amongst my guards.”
State media said at least eight people had been injured.
There were conflicting reports over the source of the explosion, with state-run Mena news agency saying a booby-trapped car had detonated as the minister’s convoy passed by.
State TV, however, said an explosive device was thrown at the convoy from the top of a nearby building just after it left his place of residence.
Pictures uploaded to the internet by witnesses showed substantial damage to a building next to the blast.
One passer-by said the explosion could be “heard from afar”.
“As you can see, cars from the minister’s convoy were destroyed and his security people took him to an armoured vehicle that transported him back to his house,” he said.
The Egyptian interior ministry said an attempt to assassinate the interior minister by “terrorist groups” had been foiled, adding that his guards had confronted and killed two of the attackers.
“We are back to the terrorism of the 1980s,” a ministry statement read. An investigation team has moved to the scene of the incident, it added.
Hundreds of arrests
This is the first attack targeting such a high-ranking government official as Egypt remains in turmoil over a showdown between the military-backed government and the Muslim Brotherhood.
The police force, alongside security forces, carried out a deadly security crackdown in the capital last month, clearing two protest camps set up by Muslim Brotherhood supporters of ousted President Mohammed Morsi.
They had rallied for six weeks demanding the reinstatement of Mr Morsi, who was deposed by the military two months ago following anti-government protests by millions of Egyptians.
Nasr City was the site of the larger of the two protest camps based outside Rabaa al-Adawiya mosque, which was dismantled in the security operation that killed hundreds of Brotherhood supporters on 14 August.
The BBC’s Bethany Bell says there has been a lot of Muslim Brotherhood activity in the area over the last couple of weeks.
Since the security clampdown, hundreds of Brotherhood supporters have been detained, including the group’s most senior leader, Mohammed Badie, and his deputy, Khairat al-Shatir.
Mr Morsi is currently being held in a secret location awaiting trial on charges of inciting murder during anti-government protests that occurred in December 2012.
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