The largest of the attacks happened in central Baghdad when a suicide bomber attacked pilgrims on their way to the shrine of the Imam Musa al-Kadhim, 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.
On the northeastern edge of the capital, in the town of Bab al-Sham, at least three mortars targeted Shiite pilgrims, killing four and wounding at least 12.
Also in Mashahidah, just north of Baghdad, at least three pilgrims were killed and eight wounded by an improvised explosive device.
Hospital officials confirmed the casualties. All officials spoke anonymously because they are not authorized to brief the media.
No one has claimed responsibility for the attacks on the pilgrims, but the ISIS militant group has been behind attacks in several of the capital's predominantly Shiite neighborhoods.