At least 54 people were killed and 90 wounded in the attack, which witnesses say occurred when a car drove up and parked in the square in front of the city's grand mosque, immediately attracting a crowd of people assuming it was a contractor looking for day labour.
"A blue car pulled into the area and dozens of people surrounded the car thinking that they were looking for workers," said Nasser Kadhim, who lost his brother in the blast and was himself wounded.
"A few minutes later the explosion happened and everything was thrown into the air."
Luring civilians next to a booby-trapped vehicle which appears to offer work or cheap food is a method used by extremists operating in Iraq.
Basra deaths
Violence has also been seen early Tuesday in the British-administrated south of the country, where a new crackdown has been launched against Shiite militias.
At least five Iraqis were killed and 15 wounded in clashes during a British operation in the centre of the port city of Basra which was targeting weapons caches, a security source said.
Basra, once relatively peaceful, has recently been riven by battles between rival militias and gangs smuggling oil, prompting British forces to step up operations.
Third deadly attack
The blast in Kufa is the third attack which has created a heavy death toll in three days, it comes a day after a market massacre killed 48 people in a small town just south of Baghdad.
In the attack on the market in the town of Mahmudiyah two car bombs and four mortars reportedly hit the market before gunmen in six cars randomly opened fire. Three of the attackers have been arrested.
On Sunday, a suicide bomber blew destroyed a coffee-shop used by Turkmen Shiites, killing 28, in the northern town of Tuz Kharmatu.