The largest of the attacks happened in central Baghdad when a suicide bomber attacked pilgrims buying food and drinks on their way back from the shrine of the Imam Ali, located in the capital's Kazimiyah neighborhood.
Officials said at least 10 people were killed in the attack and another 25 wounded.
In eastern Baghdad, another two pilgrims were killed and nine wounded when a roadside bomb exploded on Palestine Street.
Also in Mashahidah, just north of Baghdad, at least three pilgrims were killed and eight wounded by an improvised explosive device.
No one has claimed responsibility for the attacks on the pilgrims, but the Islamic State militant group has been behind attacks in several of the capital's predominantly Shiite neighborhoods.