A suicide bomber detonated a vest and gunmen opened fire inside a restaurant near Nasiriya, capital of Dhiqar province, security sources said.
Soon afterwards, a car bomb exploded at a nearby checkpoint.
So-called Islamic State said it carried out the attacks. Shia Muslim pilgrims including Iranians were killed by the suspected militants.
According to news agency AFP, one report said the attackers were disguised as members of Hashd al-Shaabi (Popular Mobilisation) - a mainly Shia group that has fought alongside Iraqi forces against IS.
