The deadliest attack took place in the southwestern neighborhood of al-Amil when a bomber set off his explosives-laden vest in a busy outdoor market, killing seven shoppers and wounding up to 25 others, a police officer said.
Another suicide attacker on foot blew himself up among residents of the eastern neighborhood of Mashtal as they were preparing for next week's Ashoura rituals, which commemorate the 7th century death of Imam Hussein, the grandson of the Prophet Muhammad and an iconic Shiite martyr.
At least six civilians were killed and 21 others wounded, another police officer said. Three more civilians were killed and 10 wounded in a bomb explosion in a commercial area in the northern Sabi al-Bor area, police added.
Medical officials confirmed the casualty figures. All officials spoke on condition of anonymity as they were not authorised to release information.
In statements posted online, the Islamic State group claimed responsibility for the attacks in al-Amil and Mahstal neighborhood, saying they were targeting Shiites.
The Associated Press could not verify the authenticity of the statements, but they were posted on a militant website commonly used by the extremists. No one has yet claimed responsibility for the third attack, which also bore the hallmarks of IS.
Despite a series of battlefield defeats in recent months, the group still controls key areas in Iraq, including the northern city of Mosul. The Iraqi government is preparing to launch a major military operation, with air support from the U.S.-led coalition, to retake Mosul this year.
As it has lost territory, IS has increasingly turned to insurgent-style attacks away from the front lines in an attempt to distract security forces and undermine government efforts to maintain security. Violence claimed the lives of at least 1,003 Iraqis last month, including 609 civilians, according to the UN Assistance Mission to Iraq, known as UNAMI.
At least 1,159 people were wounded in September. In August, at least 691 Iraqis were killed and another 1,016 were wounded, according to UNAMI.