Vatican media reported that the Melchite Greek Catholic archbishop of Aleppo, Jean-Clement Jeanbart, and a number of priests fled to Lebanon after the August 23 attack.
The missionary news agency Fides said "unidentified groups who want to feed a religious war and drag the Syrian population into sectarian conflicts" attacked the Christian area in Aleppo.
The report said a Byzantine Christian museum and an office of the Maronite Christian faith were also damaged.
The Melchite Greek Catholic Church and the Maronite Church are Eastern Catholic Churches in full communion with the Holy See of Rome.