The attack targeted the Karrada district, a crowded commercial area frequented by young people and families after sundown during the holy month of Ramadan.
Daesh (also known as ISIL or ISIS) terrorist group has claimed responsibility for a suicide car bomb in the Karrada shopping area, in a statement circulated online by supporters of the group.
A video posted on social media showed a large blaze in main street of Karrada from the blast.
The second bombing hit al-Shaab, a popular Shiite district in the north of the Iraqi capital, leaving a number of casualties, al-Sumaria channel said, citing police sources.
Iraqi forces last month dislodged ISIL militants from the city of Fallujah, their stronghold just west of the capital that served as a launch pad for such attacks.