Salim was waiting in a convoy of at least four cars outside the occupation forces' headquarters, known as the Green Zone, when the bomb went off.
He was among at least eight Iraqis killed in the blast. Ten Iraqi civilians were also injured, according to Aljazeera's correspondent. Two US soldiers were injured.
Smoke rose from the west side of the Tigris river, as helicopters hovered over the scene. The IGC has its offices inside the heavily fortified compound.
As the current council president, a rotating position, he was the highest-ranking Iraqi official killed during the US-led occupation of the country.
Brigadier General Mark Kimmit, deputy director of operations for the US army in Iraq, told reporters at the scene that "it is our understanding that it was a suicide car bomb".
The car carrying the bomb was adjacent to the council chief's car when it exploded, one witness told AP. The witness said Salim's driver and assistant were among those killed.
The checkpoint had been crowded with civilian cars and minibuses when the bomb was detonated. More than a dozen vehicles were destroyed by the blast, which melted the asphalt of the road and covered it in pools of blood, other reports said.
Leader of the Islamic Daawa Movement in the southern city of Basra, Salim was also a writer, who served as editor of several newspapers and magazines. Salim was the second member of the IGC to be assassinated since the council was established last July.
Salim is the highest ranking Iraqi
official to be killed
Aqila al-Hashimi, one of three women on the 25-member body, was mortally wounded in September 2003, when gunmen in a pickup truck ambushed her vehicle as she drove near her Baghdad home. She died five days later.
Foreign Minister Hoshiyar Zibari told reporters on the sidelines of a World Economic Forum in Jordan the attack would not stop preparations for the handover of sovereignty to an interim Iraqi government on 30 June.
"This shows our enemies are still there and will do anything to intimidate Iraqis to derail the political process," he said.
"This will strengthen our resolve to continue the political process ... This will not derail the process."