Created in Herne Bay, on the north Kent coast, the piece features the silhouette of a young boy and a cat, framed by a boarded-up window.
It was painted between two rusted pieces of corrugated metal, which appear like curtains thrown open by the tousle-haired youngster.
Banksy confirmed the artwork - named Morning is Broken - was by him in a post to his 12million Instagram followers on Wednesday.
He shared two photos of the intact piece, along with a third showing diggers demolishing it.
The artwork appears in the image to be first part of the building destroyed.
According to regional news outlet KentOnline, the building is part of a 500-year-old farmhouse, which is being torn down to make way for new homes.
One of the workers demolishing the site reportedly told KentOnline: “We had no idea it was a Banksy.
“It made me feel sick realising it was a Banksy - we were gutted.
“The landowner watched us do it and didn’t know either.”
Banksy unveiled another piece around the Kent coast in Margate, just last month.
Titled Valentine’s Day Mascara, the mural appeared to have a theme of domestic abuse and fighting violence against women as it depicted a 1950s housewife wearing a blue apron and yellow washing-up gloves with a swollen eye and a missing tooth seemingly shoving her male partner into a chest freezer.