The Banksy artwork was lifted from the side of the house by a crane on Friday
The mural, entitled Aachoo!! appeared on the outside of a semi-detached house in Totterdown in December and was removed by a crane on Friday.
The artwork depicts a woman sneezing so hard that she loses her false teeth.
Netherlands-based auctioneers Hessink's has confirmed it will be offering the item for sale at a public auction to be held in the coming weeks.
It was spotted at the bottom of one of the steepest streets in the UK, Vale Street, on 12 December, with Banksy confirming it was his on Instagram shortly afterwards.
When viewed with the road level, it looked as if the woman's sneeze was blowing the houses over.
Hessink's is based in the city of Zwolle in the Netherlands and has a history of selling the artist's work.
Recent Banksy sales have included items created in Liverpool, including Never Liked the Beatles and Gangsta Rat.
We learn something every day, and lots of times it’s that what we learned the day before was wrong.