The piece by the world-reknowned artist appeared in Birmingham’s Jewellery Quarter over the weekend and was vandalised yesterday.
The artwork shows two reindeer painted next to a bench in a bid to highlight the homelessness problem across Britain.
In a video posted on Banksy's Instagram account, a homeless man identified as Ryan is seen lying on the bench surrounded by his possessions.
The vandal added red noses to the reindeer painted on a wall on Vyse Street after jumping barriers installed to protect the artwork.
He reportedly asked onlookers "shall I tag it?" before ignoring the crowds pleas not to.
Since the attack, Jewellery Quarter Business Improvement District (BID) has employed 24-hour security to protect the art from further vandalism and Network Rail today took the unusual step of protecting a piece of graffiti on its property.
The festive artwork was cleaned, showing one red nose instead of two, before local maintenance engineer Chris Edwards drilled Perspex sheeting into the wall to protect the image.
Jewellery Quarter BID communications and marketing manager, Steve Lovell, said: "When we learned a Banksy had appeared, we were obviously delighted.
"It is truly an incredible and thought-provoking piece, which highlighted a genuine crisis in our city.
"But we were astounded to hear it had been defaced so soon after appearing - it was only a matter of hours.
"A young guy just jumped over the barriers and sprayed two noses on it, which is inaccurate to start with as only Rudolph has a red nose.
"He was asking the crowds whether he should do it and people were begging him saying, 'Please don't do it, please don't do it'.
"We were shocked and disgusted and one of our executives tried to clean it off, but to no avail. She stayed there until quite late into the evening before he could get security to watch it overnight. They were still there this morning when I arrived for work.
"There is so much footfall past the painting so we want to protect it the best we can because we are honoured to have a Banksy here in the city."
Unveiling the work, Banksy praised the generosity of people in the city who gave Ryan food and drink while they filmed.
The post from the Bristol-based artist said: "God bless Birmingham. In the 20 minutes we filmed Ryan on this bench passers-by gave him a hot drink, two chocolate bars and a lighter - without him ever asking for anything."
Speaking about the appearance of the piece, local jewellery wax carver Martin Clarke, 52, said: "About five o'clock in the morning there was a small tent with a couple of lads in high vis.
"(I) just thought it was to do with the upkeep of the jewellery quarter, and it turned out to be a lot more."
David Golding, interim route managing director for Network Rail's Central route, said: “As a railway family our hearts go out to the homeless, especially at this time of year.
"Banksy’s wall art has captured their plight so well. It’s right we protect it so everyone can see it.
"We discourage any graffiti and we spend a lot of time removing it from around the network … but it’s not every day we get a bona fide Banksy.”