One bombing targeted pilgrims visiting Karbala to celebrate the Shiite Muslim festival of Arbaeen, police told the Kuwait News Agency KUNA.
Arbaeen is the one of the largest pilgrimage gatherings, attracting more than 10 million people.
Iraqi security and military forces are now on alert in Karbala and other nearby cities.
It was the latest of several terrorist attacks across Iraq this week that have killed at least 118 people and wounded 450 others.
Meanwhile, in a separate attack Thursday, a suicide car bomb targeting a police checkpoint in Baquba killed at least four people and wounded 33 others, police officials said.
Two of the dead and nine of the wounded were police officers, officials said.
Authorities said the Baquba attack bore the hallmarks of al-Qaida, CNN reported.
Suicide bombers hit a pair of locations in Diyala Province, one of Iraq's constituent governorates, Wednesday, killing at least 16 people and wounding nearly 100 others, authorities said.
A suicide bombing that targeted a recruitment center in Tikrit Tuesday killed 65 and wounded 160.
Notable deaths of 2014 [PHOTOS]
India's satellite approaches Mars