The bombings, which took place at around midday, also wounded at least 50 people, the officials said.
The deadliest attack hit the Shaab area in northern Baghdad, killing at least 15.
Interior ministry spokesman Saad Maan said it was carried out by a female suicide bomber, while a police colonel said a roadside bombing was followed by the suicide attack.
A car bombing in the Rashid area of southern Baghdad killed at least three more people, officials said.
The bloodiest day was last Thursday, when triple car bombings in northern Baghdad killed at least 94.
Attacks in Baghdad decreased following a June 2014 offensive by IS that saw the group's fighters focus on holding territory and fighting battles in other areas.
But Iraqi forces have regained significant ground from IS, and the frequency of attacks in the capital has increased in recent weeks.
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