Nine Iranian pilgrims and an Iraqi assistant driver have sustained injuries in the attack, three of whom are in serious conditions, said Morteza Aqaei, a senior Iranian pilgrimage official.
Seven people have been transferred to a local hospital in the city of Al-Balad, and others to Kadhimiya hospital, he added.
A woman, in serious condition, has also been transferred to a hospital in Baghdad.
The pilgrims were from the Iranian city of Parsabad Moghan in Ardabil province, north-west of Iran.
On the type of the attack, some media reports have described it as an improvised explosive device (IED) that exploded in the roadside, but there were also reports that the terrorist have opened fire on the bus.