The attack took place early Monday when a suicide bomber blew up his explosive vest at the restaurant in the city of Nassriyah, Xinhua cited the source as saying.
The attacker apparently targeted members of a Shia paramilitary unit, known as Hashd Shaabi, or popular mobilisation, who were having breakfast at the time, the source said.
Many civilians were also among the killed and injured, the source added.
No group has so far claimed responsibility for the attack, but the Islamic State (IS) militant group is believed to be behind such attacks, which usually target crowded areas like markets, cafes and mosques.
Iraq has been suffering from a wave of violence since the IS terrorist group took control of parts of its northern and western regions in June 2014.
A UN report estimates that more than 22,300 people were killed or injured in armed conflict in Iraq in 2015 alone.