The attacks occurred within minutes of each other near a hotel housing foreign journalists.
At least one apartment building nearby collapsed and firefighters and soldiers were searching for any residents trapped in the rubble.
The blasts also took place near an Interior Ministry building where U.S. soldiers last week said they found some 170 prisoners, many of them showing signs of malnourishment and torture.
Iraqi authorities have promised to investigate. On 17 November, Interior Minister Bayan Jabor said the allegations had been exaggerated, and that only a handful of detainees showed signs of abuse.