St Elijah's monastery stood on a hill near the northern city of Mosul for 1,400 years, BBC online writes Wednesday.
But analysts said images from the air suggested it had been demolished between August and September 2014, two to three months after IS (Islamisk Stat) captured Mosul.
IS has targeted Christians in Iraq and neighbouring Syria, seizing their property and forcing them to convert to Islam, pay a special tax or flee.
The group has also demolished a number of monasteries and churches, as well as renowned pre-Islamic sites including Nimrud, Hatra and Nineveh in Iraq and Palmyra in Syria.
St Elijah's Monastery, or Deir Mar Elia, was believed to have been constructed by Assyrian monks in the late 6th Century. In 1743, its monks were given an ultimatum by Persian forces to convert to Islam. They refused and as many as 150 were massacred.
More than 100 churches and monasteries have been razed to the ground in Mosul and the predominantly Christian villages surrounding it.
The militants have targeted minorities and destroyed their places of worship. Those Christians who have remained in these areas have been forced to choose between conversion and execution.
The images showed "that the stone walls have been literally pulverized", said a source. "Bulldozers, heavy equipment, sledgehammers, possibly explosives turned those stone walls into this field of grey-white dust. They destroyed it completely", according to BBC
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