The two car bombs went off about 10 minutes apart late Saturday in the Karrada district, known for its restaurants, cafes and ice cream parlors.
Police said the dead and wounded were mainly shoppers and people commemorating the death of Imam Ali, a key figure in Shiite Islam.
Two traffic policemen were among those killed. Sunday's claim of responsibility by the IS group is similar to previous claims this past week, in which the militants characterized the attacks as a response to fighting in the western Anbar province.