Witnesses described widespread panic as people tried to carry the dead and wounded through a thick crowd of pilgrims packed shoulder to shoulder.
Some were injured as people tried to run from the blast site, said Kareem Madhi, a pilgrim from nearby Hillah.
"I saw a fireball and then black smoke raising," he said. "The security measures are unable to protect these huge numbers of pilgrims."
The other blast took place at the Khan Al-Ruboo area outside the city.
Hours earlier, two separate roadside bombs targeting the pilgrims exploded in Baghdad, killing one and wounding seven others, a security official in the Iraqi capital said.
The latest incidents raised fears of a spike in attacks by suspected Sunni insurgents when the pilgrimage culminates on Friday.
Arbaeen is a Shia religious observation that occurs 40 days after the Day of Ashura, the commemoration of the martyrdom of Hussein bin Ali, the grandson of Prophet Muhammad.
Thousands of troops and police have been deployed to protect worshippers as they walk towards the Imam Hussein shrine.
On Monday, at least 54 people were killed and more than 100 injured in an attack on the pilgrims by a suspected female suicide bomber in Baghdad.
'Weak' prime minister
Saad al-Muttalibi, an adviser to the Iraqi council of ministers, told Al Jazeera: "Unfortunately, the security system in place was unsuccessful in stopping the vicious attack by the terrorists.
"The terrorists aim is to undermine security and undermine the trust of the people in the government aimed at the coming elections.
"The security forces need to be more proactive and more aggressive in fighting these Wahhabi groups.
"The prime minister [Nouri al-Maliki] hands are completely tied, putting him in a very weak position to question his ministers and hold them accountable for their misconduct," he said.