"They were just handing the trophy to the winners, the suicide attacker blew himself up in the crowd," a police captain from the village, Al-Asriya, told AFP.
The village is near Iskandariyah, a town about 40 kilometres south of the capital.
The police captain said more than 65 people were also wounded in the blast.
A medic at Iskandariyah hospital confirmed the toll and told AFP that the attack took place around 7 pm.
"The mayor died in hospital as a result of the serious wounds he suffered in the blast," the medic said.
There was no immediate claim taking responsibility for the blast but nearly all such attacks recently were carried out by the Islamic State (IS) group.
Iskandariyah is part of a mixed Sunni-Shiite area south of Baghdad which was once dubbed "the triangle of death" and was badly affected by sectarian violence last decade.
Pushing back IS in this region after the jihadists took over large parts of the country in 2014 was one of the priorities of the government and allied Shiite militias.
Further south, at least 47 people were killed when a truck bomb exploded at a checkpoint at the entrance of the city of Hilla on March 6.
The attack was the deadliest car bomb explosion in Iraq this year.
The jihadist group has been losing territory steadily in Iraq for almost a year.
In the most recent operations, Iraqi forces have been gaining ground in the western province of Anbar and have just begun their reconquest of the province of Nineveh.
Observers have warned that, as their self-proclaimed "caliphate" shrinks towards extinction, IS fighters are likely to revert to their old guerrilla tactics and ramp up suicide attacks on civilian targets.
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