The attack, which claimed the lives of many children and injured 132 people, occurred early on Sunday in central Baghdad's majority-Shiite Karrada district, the Al Jazeera news channel reported, citing its own sources.
The early morning attack claimed a large number of casualties as many Iraqi families were on the streets during the last days of the holy month of Ramadan.
The attack was followed by a second explosion. An improvised explosive device went off the also majority-Shiite Shaab area of the Iraqi capital. The blast killed five people and injured 16, according to reports.
The attacks comes just a week after the Iraqi army announced the liberation of Fallujah, which has been under Daesh control since 2014.
The Daesh is a militant jihadist group, which is outlawed in many countries, including Russia, overran large parts of Syria and Iraq in 2014 amid the ongoing civil war in Syria.