Game Changer appeared at Southampton General Hospital during the first wave of the coronavirus pandemic.
The anonymous graffiti artist is now auctioning the original canvas to raise funds for the NHS, with a reproduction of the work to remain in the hospital.
The painting has a pre-sale estimate of between £2.5 to £3.5m.
It shows a young boy kneeling and playing with superhero dolls.
While Batman and Spiderman are discarded in a bin, the child clutches a figure of a masked nurse wearing a cape.
The image, which measures 1m (3ft) x 1m, was hung in collaboration with the hospital's managers in a foyer near the emergency department.
Auction company Christie's said the painting "offers an image of hope" and represents a "personal tribute to those who continue to turn the tide of the pandemic".
Katharine Arnold, of Christie's, added: "Game Changer is a universal tribute to all those fighting worldwide on the front line of this crisis.
"The work pays tribute to the strength and resilience of those who have demonstrated true leadership throughout the pandemic, the staff of our vital NHS", she added.
She also described Game Changer as a "beacon of light for the staff and patients" at the hospital.
When the picture was first unveiled, a note said: "Thanks for all you're doing. I hope this brightens the place up a bit, even if it's only black and white."
Game Changer will be seen outside of the hospital for the first time when it goes on display at Christie's headquarters in London from 8 to 15 March, ahead of the auction on 23 March.
Banksy's latest artwork appeared on the wall of Reading Prison on 1 March, which shows a prisoner escaping on a rope made of bedsheets tied to a typewriter.
Be nice to geek’s, you’ll probably end up working for one.