A church worker who works at the monastery told Aid to the Church in Need a Mass service had coincidently been moved to another church nearby when the bomb struck.
He said: "On Saturday 10th, at 5.45 pm, a missile hit the Jesuit monastery where our office is located.
"I heard a violent explosion, followed by a second. I threw myself on the ground and a third explosion followed. After a few minutes of silence, I left my office and I saw rubble everywhere.
"We thank God that the daily Mass scheduled at that time was moved to a different location and was held at the Franciscan church."
The building received extensive damage with broken glass and rubble scattered everywhere.
The news emerges after pro-government forces have taken back control of the majority of the besieged city which has been split between rebel and government control since 2012.
The Jesuit monastery is located in the north-west part of the city in an area controlled by government forces and away from the epicentre of the fighting in the east.
Charities working in the region have reported that around 50,000 civilians are caught up in the violence.