The bomber detonated his explosives’ vest at the service in the Iraqi capital’s southwestern suburb of Hay al-Amal, said a police official.
At least 46 people were wounded in the explosion.
The militia fighter was killed in battle against the militant group in Iraq’s western Anbar province, police said.
No one immediately claimed responsibility for the attack, but the Islamic State militant group has frequently targeted large Shi’ite gatherings. The radical Sunni group believes that Shi’ites are apostates who have strayed from Islam.
Following its blitz last year, the Islamic State group, which splintered off from Iraq’s al-Qaeda branch, now holds about a third of Iraq and neighboring Syria in its self-declared caliphate.
Since the emergence of IS extremists, Baghdad has seen near-daily attacks, with roadside bombs, suicide blasts and assassinations targeting Iraqi forces and government officials, with significant casualties among the civilian population.
The violence has killed hundreds and displaced tens of thousands of Iraqis.