Dozens more have been killed and wounded in bomb attacks in other cities across the country, reports say.
In the central city of Karbala, four people were killed when two car bombs targeting Shia pilgrims exploded.
There has been a spike in attacks across Iraq in recent weeks. June was the bloodiest month in the country since US troops withdrew in December.
It is thought the Karbala blasts, which also injured at least 30 people, were aimed at pilgrims gathering ahead of a religious ceremony on Friday.
The Shia community is celebrating the Shabaniyah festival, which marks the anniversary of the birth of key Shia Imam.
The Diwaniya blast was near a mosque where pilgrims were gathering to make the journey to Karbala, according to Reuters.
Police have imposed a partial curfew and closed all entrances to the city, the agency says.
There were also blasts in the Sunni city of Taji, the site of a military base 20km (12 miles) north of Baghdad.
Three people were killed there - including a policeman, and 15 were injured, according to news agency AP.
No group has claimed responsibility for the blasts.
The chairman of the Qadisiyah provincial council, Jubair al-Jabouri, blamed the Diwaniya attacks on Sunni insurgents linked to al-Qaeda.