More than 20 people were injured in addition to those who died.
A second bomb which exploded later in a predominantly Shia area north of the capital also caused several injuries.
The bombings come a week after Iraqi security forces recaptured the city of Falluja from Islamic State militants.
Authorities say the city was used as a launching pad for attacks on Baghdad by IS.
The jihadist group on Saturday claimed responsibility for the suicide car bomb in Karrada - which caused a huge street fire on the main street - in a statement distributed online by supporters of the hardline Sunni group.
The car bomb went off as people were eating out late during the Muslim fasting month of Ramadan, which ends next week.
IS still controls large swathes of territory in the country`s north and west, including Mosul, Iraq`s second largest city.
But the group has been under pressure in Iraq and in neighbouring Syria, where it has been targeted by government forces and US-backed rebels.
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