An interior ministry official said that at least three mortar rounds were fired after the car bomb was detonated in the Karrada district on Thursday.
At least 101 people were reported injured in the attacks.
A witness said two buildings had been badly damaged in the blasts and shops along the street had caught fire.
The mortars were fired across the Tigris river into predominantly Shia Karrada from the mainly Sunni al-Dura area, a security source said.
Although there have been bombings in Karrada before, it has been one of the few relatively stable districts of the capital.
In the al-Mansour district of western Baghdad, assailants killed four security guards outside a Sunni mosque in a drive-by shooting.
The violence comes two days after George Bush, the US president, approved plans to send more US and Iraqi troops onto Baghdad’s streets to combat rising sectarian violence.
An average of 100 people a day have died in sectarian violence in the past few weeks.