A statement shared by social media accounts loyal to the terrorist organization said that a terrorist known as "Abu Hamza al-Intihari (the Suicidal)" blew himself in a Shiite gathering.
According to ISIS, the attack resulted in 30 dead and 35 injured.
The Commander-in-Chief of the Iraqi Armed forces, PM Mustafa al-Kadhimi, held an urgent meeting with the Baghdad Operations Command and senior security, military, intelligence commands.
A breif statement by PM al-Kadhimi's office said, "the meeting is held in the wake of the Sadr City explosion."
The death toll from the bomb attack that took place in the east of Baghdad on Monday, has risen to 35, a security source said, with 57 injured at least.
The attack took place in a busy market of Sadr City, the source said. It happened a day before the Eid al-Adha holiday when the market is crowded with shoppers.
“A terror attack using a locally-made IED (improvised explosive device) in Woheilat Market in Sadr City, in east Baghdad, left several victims dead and others injured,” Iraq's Security Media Cell reported.
Women and children were among the dead and some shops burned down as a result of the explosion.
There was no immediate claim of responsibility but the armed group ISIS has claimed similar attacks in the area before.
The source said that the attack was executed by a female suicide bomber wearing an explosive vest.
It was the third time this year that a bomb hit a market in the densely populated neighbourhood. In April, at least four people were killed in a car bomb attack in Sadr City. That blast was caused by an explosive device attached to a parked car at the market.
Prime Minister Mustafa al-Kadhimi placed the commander of the federal police regiment responsible for the area of the marketplace under arrest, according to an Iraqi military statement. It also said an investigation was launched.
Once an almost daily occurrence in Baghdad, large bomb attacks have slowed since ISIS was defeated on the battlefield in 2017.
Attacks persist, however. In January, more than 30 people were killed in a twin suicide bombing in a busy commercial area in central Baghdad. It was the deadliest bombing in three years to strike Iraq’s capital.