"Three suicide bombers tried to cross the checkpoint at Adan Square" in the Kadhimiyah neighbourhood, said Baghdad Operations Command spokesman Sa'ad Ma'an on Sunday.
The attack took place at around 5:30 pm (1430 GMT) Saturday on the square, one of the main access points for the Shiite shrine of Kadhimiyah, which attracts many visitors on Saturdays.
Sa'ad Ma'an said security forces at the checkpoint engaged the attackers and shot dead one of them, while the other two blew themselves up, the AFP news agency reported.
A police colonel said one of the explosions was caused by a suicide car bomb.
He said at least 24 people were killed and 61 wounded. A source at the nearby Kadhimiyah hospital and an interior ministry official confirmed the casualty toll.
Baghdad Province of ISIL, which has controlled swathes of Iraq since last year, claimed responsibility for the attack, said a US monitoring group.
The ISIL affiliate tweeted that two bombers, Abu Hudhayfa and Abu Aisha, detonated their explosive belts, one after the other, at Shiite gatherings in Kadhimiyah, according to SITE Intelligence Group.
Adan Square has been repeatedly hit by attacks. More than 20 people died in a suicide bomb blast there in February.
According to figures released by the United Nations Mission in Iraq on Thursday, a total of 717 Iraqis were killed and another 1,216 were injured in acts of terrorism, violence and armed conflict in September.
The Baghdad governorate alone accounted for 257 of the deaths.
The UN says its figures only account for the casualties that can be verified and are likely far below reality.