A woman with a full body veil is alleged to have been the suicide bomber.
A woman suicide bomber killed at least 31 people and wounded 35 in a crowded market in the town of Musayab, 80 km (50 miles) south of Baghdad, on Friday, security sources said.
Daesh claimed the attack, as well as one at the main bus station in the Shi'ite holy city of Kerbala, just west of Musayab, which killed three people and wounded 15.
A security officer said the bomber in Musayab was a woman and had hidden the bomb under her full-body veil.
Islamic State's statements identified both bombers as men.
The hardline Sunni Muslim insurgents declared a self-styled "caliphate" over parts of Syria and Iraq three years ago but are now on the brink of losing Mosul, their de-facto capital in Iraq, to a U.S.-backed Iraqi offensive launched in October.
They are also on the back foot in Syria, retreating in the face of a U.S.-backed, Kurdish-led military coalition attacking Raqqa, Daesh's urban redoubt there.