In a statement posted on social media, IS said yesterday night's operation was dubbed "The Pounce of the Monotheists on the Chests of the Apostates".
The blasts, several of which were caused by suicide bombers, left 23 people dead and 68 wounded in Shiite neighbourhoods of Baghdad, according to police and medical sources.
The string of attacks was one of the worst in recent weeks in Baghdad, where it had been feared IS would ramp up bombings during the holy Muslim fasting month of Ramadan.