One attacker detonated his explosive vest inside the restaurant, south-west of Nassiriya, while three to four other attackers opened fire at the people inside, police sources said.
Sources at city hospitals said four Iranian citizens were among those killed. Police said the death toll could rise as several of the wounded were in a critical condition.
Bomb attacks in southern Iraq, where the bulk of the country’s oil is produced, are relatively rare.
No group immediately claimed responsibility, but the attack occurred with Iraqi forces battling to defeat Daesh militants in areas under their control.