The attack took place at around 7 p.m. (1700 GMT) on Thursday against the town of Musayyib.
Police said it appeared the rounds came from the nearby town of Jurf al-Sakhar.
Nobody immediately claimed responsibility for the attack, but Iraqi officials lay the blame on al-Qaeda-linked militants, who had carried out similar attacks in the past.
On Tuesday, a parked car bomb in the town killed five civilians and wounded 13 others, authorities said.
Also on Tuesday, several explosive-laden cars detonated across Baghdad, targeting the city's Shia districts.
One of the bombs ripped through a bus station in the capital's neighborhood of Baiyaa and another went off in a commercial area in the affluent district of Karrada.
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