The bombings came on Monday in quick succession near the office of the police crime investigation unit in the central Karrada district, security officials said.
At least 10 policemen were among those hurt in the attack.
Fighters opposed to the US-supported government have continued to launch deadly attacks across Iraq, although the overall level of violence in the country is at a four-year low.
Last week, five people were killed and 17 injured in a bomb blast outside an ice-cream shop in Baghdad.
Also on Monday, Iraq's deputy oil minister was wounded in a bomb attack outside his house, security officials told the AFP news agency.
The bomb detonated as Saheb Salman Qutub was about to leave his home in Baghdad's northern Ataifiyah neighbourhood, they said.
Agencies
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