The female assailant blew herself up on Friday in Musayab, just east of the holy Shia city of Karbala, killing 30 civilians and wounding another 35.
Initial reports said the incident either happened in a market or bus station. Security forces said the attacker managed to hid the explosive under her full-body veil.
The attack follows Isis' bombing of a Baghdad ice cream parlour last month that left 25 civilians dead.
Isis has called for increased attacks on unbelievers Ramadan, a period in which it says the rewards for jihadi in heaven are multiplied.
Friday's events in Iraq mark the fifth major attack worldwide claimed by the group since the holy month began on 27 May.
Twin suicide bombs in Tehran, the car-ramming and stabbings in London Bridge, the Baghdad ice cream shop and storming of a casino in Manila have all been claimed by Isis, as well as the attack on an Ariana Grande concert in Manchester on 22 May.
Isis continues to lose control of territory across Syria and Iraq in the face of US-backed operations to destroy its so-called caliphate.
Experts believe it will increasingly turn towards insurgency and terror tactics around the world to prove its enduring legitimacy. Iraqi civilians have borne the brunt of many such attacks since Isis swept across the country three years ago.Reuse content