Ali al-Haidri escaped unhurt when an explosion rocked his convoy as he was travelling through the capital.
The blast killed at least one bystander and three of al-Haidri's bodyguards were hurt in the attack in the al-Adl neighbourhood.
Armed assailants opened fire on the convoy seconds before the explosion, sources told Aljazeera.
The governor's BMW appeared intact, but a car next to it was totally burned and there was a small crater in the pavement and the street.
Meanwhile, the son of a governor for the northern Iraqi province of Niniveh was killed on Tuesday in the city of Mosul, police and medical sources said.
Leith Duraid Kashmula, 19, was shot several times in the chest by unknown attackers as he was alone in his car in western Mosul, said media adviser for the governorate Hazim Gallawi.
Senior Iraqi officials have regularly come under attack. Last month, a roadside bomb was aimed at the education minister's convoy and a car bomber targeted the environment minister. Both ministers survived the attacks unscathed.
Meanwhile, a US soldier was killed and another wounded when a roadside bomb hit their military convoy near Baghdad, the US military said on Tuesday.
A roadside bomb hit the US
military convoy, killing one
The attack occurred at 11.45pm (1945 GMT) on Monday.
Another bomb went off at 7.50am in Sadr City, as a US convoy passed by, but there were no casualties, a military spokesman said.
Elsewhere, two Iraqi explosive experts were wounded as they tried to defuse a roadside bomb in Baquba, north-east of Baghdad, said national guardsman Umar Thair.
On Monday evening, eight Iraqis were injured after violent clashes erupted between unknown armed men and US forces in Ramadi city, Aljazeera learnt.