The attack on the fighters, known as Sahwa, near a military base in the Madain area also wounded at least 48 people.
It was unclear how many of the victims were Sahwa fighters.
There was no immediate claim of responsibility for the attack, but suicide bombings are a tactic almost exclusively employed by Sunni extremists in Iraq, including ISIL group.
ISIL launched a militant offensive that has overrun several swathes across Iraq since June.
Now Sunni fighters, including the Sahwa and other armed tribesmen, again have an important role to play in the fight against ISIL.
The Iraqi 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, though the necessary law has yet to pass parliament.
Iraqi security forces backed by Kurdish forces, Shiite fighters and Sunni tribesmen have clawed back some ground from ISIL.