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Mr Ibrahim, Saddam Hussein's number two in Iraq's ruling council, narrowly escaped assassination on Sunday after two grenades were thrown at him.
The Iraqi news agency said Mr Ibrahim, the vice president of the Revolutionary Command Council (RCC), escaped unhurt after being attacked in the Shi'ite holy city of Karbala, south of Baghdad.
The town has in the past been known as a base of opposition groups.
Several bodyguards and bystanders were wounded after assailants threw the grenades at Mr Ibrahim as he was getting out of his car to attend a religious ceremony.
The agency said he "was the target of a cowardly assassination attempt" but "no harm came to him".
It said investigations were already underway to find the perpetrators.
Our correspondent Richard Downes in Baghdad says the attack was an extremely serious attempt on the number two in the country who on occasions deputises for President Saddam Hussein and hails from the same region.
Reports said the attack occurred on Sunday morning as Mr Ibrahim arrived at the mausoleum of Imam Hussein for a ceremony marking the imam's birthday.
Imam Hussein, the grandson of the Muslim prophet Mohammed, is especially revered by Shi'ite Muslims.
The agency said Mr Ibrahim continued with his visit and delivered a speech on behalf of President Saddam.
Mr Ibrahim: One of the inner circle
The attack is the first on a senior Iraqi figure reported by the government since December 1996 when the president's eldest son Uday was badly wounded in an assassination attempt in Baghdad.
Mr Ibrahim, a former interior minister, is a powerful figure within Iraq's ruling elite and serves as a deputy commander of the Iraqi armed forces.
He has been number two in the RCC, the country's highest authority, since 1979 when Saddam Hussein assumed the Iraqi presidency.
Our correspondent Allan Little says he is a very loyal lieutenant and a very prominent figure in the country. However, he is not thought to be a possible successor to the president.
Karbala was one of the main cities to rise up against Saddam Hussein after the 1991 Gulf War defeat.
It was controlled by anti-Saddam militants for several days before loyalist troops put down the uprising.
The attack comes after the United States and Britain vowed to step up support for the Iraqi opposition in a bid to oust President Saddam from power following the recent stand off over weapons inspections that nearly led to military strikes.
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