Hilla was the scene of one of the deadliest attacks in the Iraq war in February 2005 when a suicide car bomber killed 125 people.
The Hilla attack capped a day in which at least 14 other people were killed in bombings and mortar attacks against Shia and Sunni targets in Baghdad.
In Baghdad's Karrada district an explosion on a minibus killed at least six people and wounded at least eight.
Police said that the explosive was left in a bag by a passenger who got off the bus just before it detonated.
"We heard a big explosion and we rushed to the street to see the bus on fire and some wounded people jumping from the bus and falling on the ground," said Jamal Ali, a witness.
"They were crying for help and some residents took them to the hospital without waiting for the ambulances. Only the driver was unhurt."
At least six people were killed and 12 injured when a car bomb exploded at a bus stop near a busy shopping area around Rusafi Square on Rashid Street in central Baghdad, police said.
Police also said two people died and nine were wounded as 10 mortar bombs hit Adhamiya, a mainly Sunni area in northwest Baghdad.
Thousands of US troops are being sent to Baghdad to help Iraqi security forces in an attempt to avert a sectarian civil war between Iraq's Shia majority and Sunnis once dominant under the late Saddam Hussein.