Mohammed al-Shammari, a doctor from the nearby town of Iskandiriyah, confirmed the death toll.
The fighting in Jerf al-Sakhr brings an end to a period of calm in the town, which was promoted by the anti-al-Qaeda armed groups.
Speaking before news of the early morning clashes broke, Salem al-Saleh Meslmawe, Babil’s governor, said that US forces would hand over security control of the province to Iraqi forces on Thursday.
Major General Fadhel Radad, Babil's police chief, also confirmed the plan to transfer the province to Iraqi forces.
"The security forces in the province are ready to take control and these days they are handling the security efficiently in collaboration with the citizens," Radad said.
If the handover goes ahead, it will become the 12th of Iraq's 18 provinces to be transferred to forces receiving orders from the government in Baghdad.
Baghdad, Diyala, Salaheddin, Nineveh, Kirkuk and Wasit remain under US control.
A US military spokesman confirmed that preparations were being made to transfer Babil to Iraqi command but declined to give a date.
A series of attacks occurred across Babil in the wake of the US-led invasion in 2003, with frequent sectarian attacks on Shia pilgrims committed by Sunni fighters linked to al-Qaeda.
At least 117 pilgrims were killed and 200 injured in a suicide attack in Hilla, Babil's capital, in March 2007.