The bomb hit a crowd of labourers as they gathered close to a Shia shrine in the centre of the city at 0730 local time (0330 GMT), officials said.
Witnesses said the labourers seeking work had gathered around a minibus which then exploded.
Shia Muslims in Kufa, 160km (100 miles) south of Baghdad, have been the frequent targets of attacks.
Nasser Kadhim, who lost his brother and was injured in the blast told the AFP news agency that a vehicle pulled over and dozens of labourers surrounded it, expecting to be offered work.
Some reports said the minibus had filled up with volunteers and was pulling away as it blew up.
Policemen who arrived at the scene were pelted with stones and fired shots into the air to disperse the crowds, Reuters reported.
Anger and mistrust
The blast took place close to the golden-domed mosque in Kufa, a key Shia pilgrimage site.
It marks the site where Imam Ali, cousin and son-in-law of the Prophet Muhammad, is said to have been mortally wounded.
Monday's attack on Mahmoudiya left at least 48 deads.
His Mehdi army militia is widely accused by Sunnis of being behind sectarian violence - including a brutal attack on a Sunni suburb in Baghdad nine days ago in which dozens of Sunnis were killed.
The bombing comes a day after at least 48 people were killed and more than 60 injured in a gunfire and mortar attack on a market in the town of Mahmoudiya, south of Baghdad.
Most of the victims were believed to be Shia Muslims.
Many fear tit-for-tat sectarian killings have now acquired a dynamic of their own, and that the Iraqi Shia are no longer heeding calls for restraint from their religious leaders, our correspondent says.
In a separate development on Tuesday, British troops in the southern city of Basra killed at least four members of a Shia militia, Iraqi officials said.
At least 10 militia were injured in the clash, which took place during an operation to search for weapons.
Correspondents say it is the latest operation in a British military campaign against the Shia militias which operate in Basra.
Later on Tuesday, Iraq's national security advisor, Muwaffaq al-Rubaie, said Iraqi forces had captured four members of a militant group linked to al-Qaeda in Iraq - the organisation run by Abu Musab al-Zarqawi until he was killed in June.
The group, known as the Omar Brigade, has been blamed for a bomb attack in early July which killed 60 people in Sadr City, a poor Shia area of Baghdad and a stronghold of the radical Shia cleric Moqtada al-Sadr.Last Mod: 20 Eylül 2018, 18:16