Two police spokesmen in the area said an explosive device planted on the bus detonated at a northern entrance to the city, setting fire to the vehicle.
They said the wounded were rushed to hospital.
There was no immediate claim of responsibility for the blast.
Such attacks in the mostly Shi'ite Muslim south of Iraq have been rare in recent years, especially after the territorial defeat of Islamic State in Iraq in 2017 and the routing of its al Qaeda predecessors in the mid-2000s.Islamic State insurgents have continued to carry out regular attacks mostly against security forces in the north of the country, however.