The bomber attacked the fighters, known as Sahwa, while they were gathering near a military base in Madain on Wednesday to receive their pay, also wounding at least 56 people.
IS claimed the attack in a message posted online titled "Statement on the Martyrdom Operation in the Madain District", and identified the bomber as Saifeddin al-Ansari.
IS spearheaded a sweeping militant offensive that has overrun much of Iraq's Sunni Arab heartland since June, areas that Shiite-led government forces have sought local Sunni help to recapture.
The Sahwa were key to greatly but temporarily reducing the violence, but when Iraq's government took over responsibility for their salaries they were sometimes paid late or not at all.
Now Sunni fighters, including the Sahwa and other armed tribesmen, again have an important role to play in the fight against IS.
The government has distributed arms and ammunition to tribesmen, and Prime Minister Haider al-Abadi aims to establish a national guard made up of local fighters, although the necessary law has yet to pass parliament.
But major areas, especially north and west of Baghdad, remain outside government control.
