Stations of the Cross that belonged to late Primate Cardinal Cahal Daly had been placed inside St Brigid's Church in Malone Road, Belfast.
Parish priest Father Edward O'Donnell, who was bequeathed the paintings, said he did not believe the graffiti had been done by children.
In a parish newsletter he said: "Although they are now my personal property, I decided to hang them in the church for I felt, correctly, that parishioners would appreciate them as much as I do. However, I regret to say that I have had to remove the Stations as some misguided person took it upon himself/herself to draw faces on all the figures depicted on the Stations. This was not the work of a child as the drawing is rather skilfully done; nevertheless, I regard it as a desecration and as vandalism. I have asked an art restorer to investigate the possibility of restoration."
The artwork was produced by Irish artist Roy Carroll and had been left to the Belfast-based priest after Cardinal Daly died in 2009.
Fr O'Donnell has called for the person responsible to come forward and help contribute towards the cost of restoration. He added: "I don't propose to take any other action. However, the person who did this could make restitution by covering the cost of the restoration; indeed he/she has a moral obligation to do so."
News of the vandalism was included in the St Brigid's parish bulletin which was distributed during mass on Saturday night.
SDLP MLA Conall McDevitt, who is a parishioner at St Brigid's, said the congregation had been left dismayed. "It is really sad and exceptionally disappointing," he added. "It is bad enough that any artwork is damaged but particularly art work in a sacred space."
A spokeswoman for the PSNI said there was no record of the graffiti being reported to police.