The explosions happened one after another in the busy al-Sinak market. More than 50 people were injured.
Police said a roadside bomb exploded near a car spare parts shop, then a suicide bomber detonated his device among the crowd that had gathered.
Baghdad has seen frequent attacks, often targeting Shia districts.
IS released a statement saying two of its militants had carried out the bombings wearing suicide vests.
The jihadist group is under pressure from an Iraqi army offensive further north in Mosul, the last major IS stronghold in the country.
Many of the victims in Saturday’s attacks worked in spare parts shops in the largely Shia area, witnesses said.
“They were gathered near a cart selling breakfast when the explosions went off,” local shopkeeper Ibrahim Mohammed Ali told the AFP news agency.
In November, 77 people including Shia pilgrims died in a truck bomb attack in Iraq, and in July 281 people died when bombers targeted a shopping centre in the country.
IS claimed responsibility for both attacks.
The group took control of a large portion of northern and western Iraq more than two years ago but has since been driven back.
Iraqi security forces have teamed with Kurdish Peshmerga fighters, Sunni Arab tribesmen and Shia militiamen – assisted by warplanes and military advisers from the US-led coalition – to attempt to force IS militants out of Mosul, their last major stronghold.
The operation has been ongoing since 17 October.
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