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.
The attackers struck at midday local time (09:00 GMT) in stolen army vehicles.
"One attacker blew up his suicide vest inside the crowded restaurant while a group of other gunmen started to throw grenades and fire at diners," said police colonel Ali Abdul Hussain, quoted by Reuters.
At least seven Iranians were among the dead, health officials said, adding that more than 90 people were injured.
Unconfirmed reports said police officers had died in the checkpoint attack, but the total number of dead from that incident is not known.
Afterwards, rescuers cleared away burned bodies, vehicles and twisted scraps of metal from corrugated shelters.
IS are enduring defeat after defeat on front lines in both Iraq and Syria, but they remain capable of launching devastating assaults on soft targets, says BBC Middle East editor Alan Johnston.
It is still believed to have hundreds of followers prepared to carry out attacks.
However, such attacks are relatively rare in southern Iraq, and Dhiqar province has previously been spared some of the worst of Iraq's violence.
The area targeted is on a main road frequented by Shia pilgrims and visitors from Iran on their way to the holy cities of Najaf and Karbala to the north.