The road is expected to be thronged with pilgrims in coming days as millions of Shia converge on Karbala for Ashura, one of the holiest events in the Shia religious calendar.
The attack came one day after a car bomb killed 18 people in Musayib, a mixed Sunni and Shia town south of Baghdad.
The previous day, a car bomb near a Shia mosque killed 13 people in Balad Ruz, northeast of Baghdad, and fighters attacked a Shia bakery in the capital, killing nine.
The bodies of three Iraqis have been discovered in eastern Baghdad, police said on Sunday, adding they could be those of police officers or soldiers who were tortured.
"The three victims had civilian clothes, were blindfolded and had their hands tied with wire," a police officer said.
He said the victims, who were not immediately identified, had not been shot but probably tortured to death.
On Saturday, 14 bodies were discovered in and around the northern city of Mosul.