Amara's police chief was fired after the blasts, Major General Abdul-Karim Khalaf, an interior ministry spokesman.
Police also announced a 24-hour curfew in the city.
The bombs exploded along a main street in Amara and hospitals were overwhelmed with the casualties, Mohammed Saleh, a provincial council spokesman, said.
Amara, straddling the Tigris River, is the capital of Maysan province.
Located 50km from the border with Iran, it is the northernmost tip of a 16,000 sq-km triangle of marshlands where the Tigris and Euphrates rivers meet.
The city's economy is based on farm products, including rice, dates, and sheep.
During the 1980s the government built new docks at Amara, and the city is home to a Japanese-built hospital.
It was founded in the 1860s as a military outpost of the Ottoman Empire.
From Amara, the Ottomans tried to control long-standing warfare between two local tribes, the Banu Lam and the Al Bu Muhammad.
Most people were killed in the second and third blasts, police said.
Many onlookers had gathered after the first blast in a parking lot and were killed or wounded when the subsequent car bombs exploded.
Southern Iraq is witnessing a turf war between rival Shia groups, including supporters of Muqtada al-Sadr and his Mahdi Army militia, and its chief rival, the powerful Supreme Islamic Iraqi Council.
A year ago, clashes broke out between militiamen and police in Amara, prompting the dispatch of hundreds of Iraqi troops.
The attacks came just a day after a suicide car bomber targeted the offices of Iraq's former prime minister and a Sunni parliament member, killing two policemen.
Police and hospital officials said at least 12 people were wounded in addition to the deaths as a result of Tuesday morning's attack in western Baghdad's Hathiya neighbourhood.
"All the casualties are policemen. They were part of the security for the leaders staying there," an official said.
The bombing happened less than 150 metres from the offices of Iyad Allawi, the first post-Saddam prime minister, and Saleh al-Mutlaq, leader of the National Dialogue Front.
Neither politician was at their office at the time of the explosion.
In the Saidiya neighbourhood of Baghdad on Tuesday, a bomb hidden in a corpse blew up and killed an Iraqi soldier and wounded seven people, security officials said.
"The soldiers went to collect the corpse which was lying in an open area when the bomb inside it exploded and killed one soldier," an official said.
Also on Tuesday, the US military said American and Iraqi troops detained five men suspected of involvement in the assassination of the police chief in central Iraq's Babil province on Sunday.
Major General Qais al-Mamoori was near Babil's capital Hilla when a roadside bomb struck his convoy.
He was the third top Shia official to be assassinated in four months in provinces south of Baghdad amid intense rivalries between Shia groups.