Iraqi Interior Minister Mohammed al-Ghabban announced his resignation after the attack, considered the deadliest since the 2003 USA -led invasion.
The group struck again on Thursday with a triple suicide attack on a Shiite mausoleum north of Baghdad, killing at least 35 people.
One gunmen detonated his explosives belt at the marketplace outside the shrine and another at one of its gates, the source said, adding that two mortar rounds landed at the scene at the time of the blasts.
At least one gunmen blew himself up in the middle of the crowd, according to Reuters.
A statement posted on Prime Minister Haider al-Abadi's Facebook page said he had dismissed the commanders of military operations, security services and intelligence in the capital.
The suicide bomber first targeted police guarding the shrine's entrance. Scores of people were also injured in the attack.
It killed 40 people and wounded 74, health ministry spokesman Ahmed al-Rudaini said.
Small-scale bombings occur on a near-daily basis in Baghdad, and in May a string of larger attacks, many of them claimed by IS, killed more than 200 people in a single week.
Police say a third bomber was also killed before he could detonate his explosives belt.
Interior Minister Mohammed Salem al-Ghabban submitted his resignation Tuesday, but al-Abadi has not accepted it.
Prominent Shi'ite cleric Moqtada al-Sadr ordered his militia, the Peace Brigade, to deploy around the mausoleum, near Balad, about 93 kilometers north of Baghdad.
The government is highly criticized for being unable to prevent the attacks that killed around 300 innocent people.
Daesh group, an extremist Sunni group which sees Shias as "apostates", has claimed responsibility for the attack on its affiliate news agency Amaq. It is intensifying attacks as it loses territory in the country to Iraqi forces backed by USA -led airstrikes.
Observers note mounting anger among Iraqis over the government's inability to protect civilians and implement effective security measures.