Security officials said at least two people had been killed and at least 10 wounded when a remote-controlled bomb blew up Mohamed Ibrahim's convoy as it drove through Cairo..
The minister was among those who oversaw a violent crackdown on supporters of Mohamed Mursi, the Islamist president ousted by the army in July following mass protests against his rule.
Asked by reporters whether the attack marked the start of "a new wave of terrorism", Mr Ibrahim said: "What happened today is not the end but the beginning."
Mr Ibrahim said he had been informed of plans to kill him, and "foreign elements" were involved. General Abdel Fattah al Sisi, head of the armed forces, had supplied him with an armoured car identical to the one he uses himself, he said.
Security sources said three bombs planted inside a parked motorcycle had detonated as Mr Ibrahim's convoy passed by. State television reported a bomb had been thrown from a roof.
Mr Ibrahim said the "despicable attempt" on his life had destroyed four of his bodyguards' vehicles. He said one police officer was in a critical condition, and that another officer and a small child had lost their legs.
The military-backed government that took over from Mr Mursi has killed hundreds of supporters of his Muslim Brotherhood, which it accuses of committing terrorist acts,