The charred minibus was still on the road near the city on Saturday morning.
The bombing was one of the biggest attacks targeting civilians since the extremist group was declared defeated inside Iraq in 2017. The group's sleeper cells continue to wage an insurgency and carry out sporadic attacks across the country.
In the wake of the bombing, which also wounded five people, Iraqi forces have increased their presence and security measures around Karbala. Iraq's prime minister, Adel Abdul-Mahdi, said security forces detained a man suspected of leaving the bomb on the bus. The statement gave no further details about the suspect.
Speaker of Parliament Mohamad al-Halbousi expressed his frustration with the repeated "failures of intelligence agencies" to prevent such attacks. His statement added that security plans should be reviewed and intelligence gathering intensified.
On Saturday, security was tight on the roads entering Karbala, with added checkpoints searching cars.
The explosion occurred as the bus was passing through an Iraqi army checkpoint, about 10 kilometers (6 miles) south of Karbala in the direction of the town of al-Hilla.
The attack took place during a holy period marked by Shiites in Iraq between two important religious events, Ashoura and Arbaeen.
Arbaeen is the annual commemoration marking the end of the 40-day mourning period for the martyrdom of Imam Hussein, the Prophet Muhammad's grandson, a central figure in Shiite Islam.
Thirty-one pilgrims were killed and about 100 injured in a stampede in Karbala last week as hundreds of thousands of Shiite Muslims marked Ashoura, one of the most solemn holy days of the year. It was the deadliest stampede in recent history during Ashoura commemorations.
END/AP/UNB/KC