Twitter accounts known to be linked to Islamic State posted photographs showing the bombing of the ancient monastery of Mar Behnam near the predominantly Christian town of Qaraqosh.
The tombs of Saint Behnam and Saint Sarah are reduced to rubble in the images.
Mar Behnam monastery was built on the tomb of Berhnam and his sister Sarah, who were converted to Christianity by St Matthew.
The IBTimes UK website claims an expert on Assyrian monasteries in Iraq was able to confirm the photographs.
Dr Nicholas al-Jeloo told the IBTimes UK: "The place is a major site of pilgrimage, at the very origins of Christianity in the region, and it links us to our ancient Assyrian heritage - being only a stone's throw from the ruins of Nimrud, also destroyed by Isis.
"The only way I could describe it is as a work of art. It was one of the most richly carved monastery complexes in northern Mesopotamia up until today."
The monastery was run by the Syriac Catholic Church until the area was taken over by Islamic State.
IS has forced tens of thousands of Christians to flee their homes in Iraq and Syria as it sets up its own state.
The group has previously destroyed a number of churches and holy buildings across both countries.