Cecilia Gimenez, who is in her 80s, was reportedly upset at the way the fresco had deteriorated and took it on herself to "restore" the image.
She claimed to have had the permission of the priest to carry out the job.
"(The) priest knew it! He did! How could you do something like that without permission? He knew it!"
BBC Europe correspondent Christian Fraser says the delicate brush strokes of Elias Garcia Martinez have been buried under a haphazard splattering of paint.
The once-dignified portrait now resembles a crayon sketch of a very hairy monkey in an ill-fitting tunic, he says.
The woman appears to have realised she was out of her depth and contacted Juan Maria Ojeda, the city councillor in charge of cultural affairs.
Teresa Garcia, granddaughter of Elias Garcia Martinez, said the woman had painted the tunic before, but the fresco got disfigured when she painted Christ's head.
Art historians are expected to meet at the church soon to discuss how to proceed.
Mr Ojeda said: "I think she had good intentions. Next week she will meet with a repairer and explain what kind of materials she used.
"If we can't fix it, we will probably cover the wall with a photo of the painting."
The fresco is not thought to be very valuable, but has a high sentimental value for local people.