The site, which belongs to the Friars Minor of the Custody of the Holy Land, is covered in rubble after the attack on Sunday evening.
One person was inside and but was uninjured and there were no deaths.
The monastery is in the village of Yacubiyah which is near the Turkish border in north-west Syria.
It's not known who fired the missile.
Syria has been ravaged by a civil war for the past three years between government forces and rebels.