The artwork, which was first spotted on the side of a building in Bristol on Thursday, showed a young girl firing a slingshot.
Banksy confirmed he was behind the piece by posting a photograph on his official Instagram account and website on Friday morning.
However, a picture shared on social media hours later showed the words “BCC W***ERS” had been scrawled in pink across the artwork.
The graffiti appears to be a reference to Bristol City Council.
One local resident who spotted the vandalism responded: “It’s a real shame, but it was always going to happen, unfortunately.”
Kelly Woodruff, the daughter of Edwin Simons, who owns the rented home on which the artwork appeared, had earlier expressed concern at the potential for Storm Dennis to damage it.
In December Banksy created a modified nativity scene at a hotel in Bethlehem, depicting Jesus’ manger in front of the separation barrier in Israel.
Additional reporting by Press Association