"A suicide car bomb exploded in the road. The minister and the rest of us are safe and sound. Only a guard was killed," the official said by telephone from Abd al-Mahdi's home in the centre of Baghdad on Sunday.
Smoke and flames were seen rising from the scene of the blast, which occurred in the central Karada district on the east bank of the Tigris.
The area was immediately cordoned off by US troops and Iraqi forces.
Abd al-Mahdi is one of the leaders of the Supreme Council for the Islamic Revolution in Iraq (SCIRI), headed by Abd al-Aziz al-Hakim.
SCIRI, along with the Dawa party lead by interim Vice-President Ibrahim al-Jaafary, are among the main Shia parties in Iraq expected to play a pivotal role in the planned January elections.