The blast struck in the village of Shomali near the city of Hilla, 75 miles southeast of the capital Baghdad, and wounded at least 45 people.
Officials said the target appeared to have been buses carrying Iranian pilgrims heading home after taking part in Arbaeen, a major Shia holiday in the holy city of Karbala.
Falah al-Radhi, head of the provincial security committee for Babylon, the province where the bombing happened, said several buses were targeted.
“A large truck exploded among them. It was a suicide attack,” he said. “There are at least 70 dead, fewer than 10 are Iraqis, the rest are Iranians.”
IS claimed it carried out the attack in a brief statement put out by its Aamaq news agency which said the bomb was in a truck.
Up to 20 million people visited Karbala this year, and according to the Iraqi authorities around three million of them were Iranians.
Iraq had sent around 25,000 members of the security forces in and around the shrine city to protect the pilgrims from a feared IS attack.
Iraqi forces are currently driving out militants from the northern city of Mosul.
A senior commander said troops had retaken three neighbourhoods, Amn, Qahira, and Green Apartment and were expanding their foothold in Zohour.
Over the past few days, Iraqi forces said they have cut off the main supply line running from Mosul to the western border with Syria, where IS still controls the city of Raqqa.
The Iraqi government started its campaign to liberate Mosul on 17 October, with troops backed by US-led coalition airstrikes.
Coalition spokesman Colonel John Dorrian said: “The Iraqi advance on the south and southeast of the city has started to pick up some steam, which we think is a really great development.
“It is extraordinarily tough fighting, just brutal, but there is an inevitability to it. The Iraqis are going to beat them.”
Mosul was captured by IS in 2014 and is the last major urban centre still held by the extremist group in Iraq.