The building had housed the Chaldean Catholic Sisters of the Sacred Heart, who worked to help the poor and elderly.
Jihadists had been using the convent as a headquarters so there were no nuns inside at the time.
They had been forced to flee when I.S. took over the city as it advances across large parts of Iraq and Syria.
It's reported the extremists decided to demolish the building because it was a sign of Christianity and had a cross on a spire above the roof.
A video has appeared online of the destruction in which fighters are heard shouting 'Allah Akbar' [God is great] as the bomb goes off.
The nearby St Georgis Monastery has still not been touched.
