Both attacks were on foot, wearing explosives-laden vests, two police officers said.
One bomber struck in Baghdad's Bab al-Sharji area, killing eight civilians and a police officer. Twenty-one were wounded in that explosion.
The second bomber hit in al-Wathba Square, killing 5 people, including two policemen, and wounding 12.
No group immediately claimed responsibility for the attacks, which bore the hallmarks of the so-called “Islamic State” terrorist group.
The violence has killed hundreds and displaced tens of thousands of Iraqis.