In a message posted on an IS-affiliated Twitter account, the Sunni militant group says it targeted a Shiite gathering with a parked, explosives-laden truck.
Thursday's blast at the Jameela market in the over-crowded Sadr City neighborhood also wounded 125 people.
The claim says the group seeks to have the "rejectionists (Shiites) experience the same harm as their bombardments cause to our Muslim people" and vowed more attacks.
The Sunni militant group, which currently holds territory in about a third of Iraq, views Shiite Muslims, as well as other religious minorities, as apostates.
Double suicide bombing in Baghdad kills at least 16 people