Two of Sami al-Mudhafer's bodyguards were wounded and a civilian bystander was killed in the explosion on Wednesday, they said.
Interior ministry sources had earlier said it was Abdul Falah Hassan, the education minister, who escaped the bombing.
It was not clear whether al-Mudhafer himself was the target of the attack as bombings are sometimes directed at any convoy that seems to belong to Iraqi officials.
Sunni Arab fighters are waging a relentless campaign of suicide and car bombings, shootings and assassinations against the Shia-led government.
The car bombing comes at a sensitive time, as Shia, Kurdish and Sunni politicians are still struggling to form a new government nearly two months after elections held on 15 December.