IS also attacked an army position west of Baghdad, temporarily holding it and killing at least eight security personnel over the course of the day.
The two blasts near a market in the Sadr City area of northern Baghdad, at least one of which was a suicide bombing, also wounded at least 76 people, security and medical officials said.
IS, which overran swathes of territory north and west of Baghdad in 2014, claimed the attacks in a statement online that said two suicide bombers had detonated explosive belts in Sadr City.
Suicide bombings are a tactic almost exclusively used in Iraq by IS.
The jihadist group claimed twin suicide bombings targeting Shiite worshippers on Thursday that killed at least nine people in Shuala, a Shia-majority area in northern Baghdad.
IS also launched an attack on an army position in the Abu Ghraib area west of the city on Sunday, security officials said.
The jihadists attacked the position early in the morning, seizing it until government reinforcements arrived and took it back later in the day, the officials said.
The Abu Ghraib violence killed at least eight people, including both members of the security forces and allied paramilitaries, and wounded at least 22.
While attacks are still common in Baghdad, violence in the city has decreased significantly since IS launched a sweeping offensive in June 2014, after which many of its militants became occupied with fighting elsewhere.