"The explosion caused major damage to buildings and they even hurt some children," Abdul-Jabar Saad, a shopkeeper who witnessed that attack, said.
"God damn these people."
Two other people were also killed and 12 others wounded when a vehicle exploded near a market in the district of Hussainiya.
Another car bomb exploded near the Doura district, killing four people and injuring 15 more, according to police.
Interior ministry officials have declined to comment on whether the bombings were co-ordinated.
The attacks came after Iraqi forces last week put down an uprising by members of a so-called Awakening Council group in Baghdad angry over the arrest of their commander.
Although violence has fallen dramatically in Iraq since the US-led invasion in 2003, arious armed groups are still able to strike with deadly results.
At least 250 Iraqis were killed in violence in March.