Reuters television footage showed bloodstained debris from market stalls in the centre of the capital, where Baghdadis buy and sell birds and other live animals.
"I was sitting here when one bomb went off, then another three minutes later," one middle-aged man said.
Another witness said: "Many young men were wounded."
Elsewhere in Baghdad, a roadside bomb killed two people and wounded four in the eastern New Baghdad district.
Egyptian vendor killed
In the southern town of Amara, an Egyptian ice cream vendor who had lived in Iraq for the past 23 years was shot dead by suspected militia members.
Northeast of the capital, in the village of Hib Hib, mortars fell on a house, killing two people and wounding another, all from the same family.
In the Mansur neighborhood of west Baghdad, a bomb went off near a passing Iraqi army convoy, killing one soldier and wounding four.
An Iraqi army colonel, assistant to the brigade commander of the unit protecting oil pipelines and fields in the northern city of Kirkuk, was killed, together with his bodyguard, late on Thursday as he headed home, said an official with the Iraqi army.
An Iraqi soldier searches a car
at a checkpoint in central Baghdad
Also on Thursday, police reported that a lawyer and former city council member working with US forces in the southern town of Samawa was killed.