The silk relic was donated to St Peter's Church in Pwllheli, Gwynedd, by a woman with terminal cancer who used to regularly attend the church.
Fr Huw Bryant, associate priest in Bro Enlli ministry area explained in a Facebook post that the woman who donated it was actually a pilgrim.
"Not many people know that Pwllheli was once an important pilgrimage site - we tend to focus more on the ancient pilgrimage route to Ynys Enlli (Bardsey).
"But Hywel Rheinallt wrote in the 15th Century of hundreds of people coming on Mary's feast day and says "this holy town is Mary's ground." Hywel Rheinallt was a bard.
Fr Bryant said she asked "for the strength to accept her death and find peace".
He continued: "This she received and in thanksgiving organised a gift to the shrine upon her death, a piece of the veil worn by the Blessed Virgin Mary at the foot of the Christ's cross."
It is thought the 6m-long silk veil was first transferred from Jerusalem to Constantinople - modern day Istanbul.
It was then given to the Emperor Charlemagne in 876 AD by the Byzantine Empress Irene, but it is currently kept in the cathedral in Chartres in France.
Officials claim the piece given to St Peter's Church was removed from the full veil in 1829 and sealed with Spanish wax, bearing the imprint of the coat of arms of Fr Giuseppe Mancini, Archbishop of Sienna.
Clerics have said the piece of the veil comes with a certificate of authenticity.
A Mass of Celebration will be held at St Peter's Church on 19th January.
Fr Bryant said he expected the veil to attract even more pilgrims to the church.
"We are now looking at plans as to how we can house this important relic, the only one of its kind in Wales, so that it can be on permanent display for pilgrims to come and seek Mary's prayers," he said.
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