"The ministry executed 36 prisoners in Nasriyah prison after they were found guilty of (the massacre at Camp) Speicher," Xinhua news agency reported.
On June 12, 2014, fighters of the IS, comprising mostly armed Sunni insurgents, launched a surprise offensive on Iraqi security forces and captured a large part of the country's northern and western territories after government troops abandoned their posts and military equipment.
The IS fighters allegedly singled out Shia and non-Muslim cadets from Sunni ones and gunned them down at Camp Speicher in Saddam Hussein's hometown of Tikrit.
Tirkit town is around 170 km north of Baghdad.
Shortly after taking Tikrit, the IS group posted graphic images of gunmen shooting the men dead after forcing them to lie face-down in a shallow ditch.
The massacre sparked outrage across Iraq and partially fuelled the mobilisation of Shia militias in the fight against the IS, a Sunni extremist group.
Iraqi forces with the help of US-led airstrikes, retook Tikrit in 2015 and arrested dozens of militants linked with the massacre.
Iraqi Prime Minister Haider al-Abadi has attempted to fast-track the implementation of death sentences following a series of large-scale bombings in and around Baghdad in recent months.
The UN had earlier this month criticised the policy, saying that "given the weakness of the Iraqi justice system", the rushed sentences risk causing "greater injustice."
Iraq ranks among the top five countries in the world to use capital punishment, according to figures compiled by the human rights group Amnesty International.
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