Officials said that a double explosion struck near a bus station in Babil province on Thursday, killing 14 policemen and a provincal councillor.
The first bomb, in a car, was said to have exploded at about 2pm (1100GMT) in Hilla, the provincial capital about 95km south of the capital Baghdad.
Another blast came about 15 minutes later when police arrived.
The authorities said that the attacks targeted Shia pilgrims who gathered near the bus station to mark Ashura, a commemoration of the death of the Prophet Muhammad's grandson, Hussein.
In northeastern Shia area of Sadr City in Baghdad, a bomb planted near a funeral tent killed eight people and wounded another 33.
Ahmed Rushdi, a journalist in Baghdad, told Al Jazeera: "The balsts happened nearly at the same time.
"They were not by the hand of al-Qaeda - they were not suicide bombers, but mostly car bombs and bombs beside cars."
Also on Thursday, a bomb blast also killed two people and injured four others in the Shia sacred city of Karbala, about 100 kilometres south of Baghdad, police said.
On Wednesday, six people were killed and another 43 people were injured in Baghdad in three explosions targeting Shias.
Thousands of Shias are expected to converge on the central city of Karbala for the December 27 Ashura holiday to mourn the Prophet Muhammad's grandson, Imam Hussein, killed by armies of the caliph Yazid in 680 A.D..
More than 25,000 security personnel have been assigned to protect pilgrims during the celebrations.