Mohammed al-Nasiry, a journalist in Nasiriya, told Al Jazeera: "It's the first time in three years since we've had such a big explosion in Nasiriya.
"High security measures have been taken by authorities, bridges are being closed and the city is under semi-curfew. There are fears of another suspicious car that may explode at any time," he said.
Nobody has claimed responsibility for the attack, but car bombings are regarded as being a standard form of attack by al-Qaeda in Iraq.
Talib al-Hassan, the governor of Nasariya, said : "We accuse al-Qaeda ... the security forces are working to get precise information."
The local police chief was sacked following the attack, and an inquiry launched to determine whether police could have prevented it.
Hussein Salim, a witness, said the market was supposed to be guarded by the police, adding: "The police neglected their job.
"How could the car enter the market? It was crowded with people."
The death toll from the explosion could rise, Akram al-Tamimi, the media manager of the Nasariya provincial council, said.
The attack comes just weeks before US troops are due to pull out of all towns and cities across the country.
Fereydun Rafiq Hilmi, an Iraqi political analyst, told Al Jazeera: "... the philosophy of a car bombing is to create havoc and a feeling of insecurity, a situation where the government look weak, the forces that are actually keeping law and order, look weak.
"Violence is escalating. Even today it is not the only bombing or violent attack that we have seen. There have been attacks all over Iraq, in Baghdad and Mosul and Fallujah and in other places. The shootings and a grenade here and there is not reported.
"This happened in an area which has been quiet for some time and that is why I think we have this in the news today whereas the others are ignored."