The claim was made in a statement posted on a Twitter account frequently used by the extremist group. It did not mention the nationality of the attacker.
Yesterday's attack targeted the funeral of the father of two members of pro-government Sunni militias. The Islamic State group frequently targets Iraq's Shiite majority as well as Sunnis allied with the Shiite-led government.
The bomber showed up at the funeral disguised as a Shiite, with a religious flag and a portrait of a Shiite imam, according to Hussein Ali, a local resident who said he witnessed the attack.
Retired Brig Gen Abbas Hussein had joined the Badr Brigades, a powerful Shiite militia, after the IS group captured vast swaths of northern and western Iraq over the summer, said fighter, who spoke on condition of anonymity because his militia had not authorised him to speak to the press.
The Sunni IS group controls around a third of both Iraq and neighboring Syria, where it has declared an Islamic caliphate and imposed a violent form of shariah law.