The artwork, which is called 'Game Changer', shows a boy dressed in dungarees playing with a toy nurse who is in a flying superhero pose along with a superhero cape.
There are two toy figures of Batman and Spiderman in a basket on the floor next to him.
The picture is on display in Southampton General Hospital, where Banksy left a note for workers saying: "Thanks for all you're doing. I hope this brightens the place up a bit, even if it's only black and white."
Once lockdown is lifted, the artwork will be sold to raise money for the NHS.
Paula Head, chief executive of University Hospital Southampton NHS Foundation Trust, said: "Here at Southampton, our hospital family has been directly impacted with the tragic loss of much loved and respected members of staff and friends.
"The fact that Banksy has chosen us to recognise the outstanding contribution everyone in and with the NHS is making, in unprecedented times, is a huge honour.
"It will be really valued by everyone in the hospital as people get a moment in their busy lives to pause, reflect and appreciate this piece of art.
"It will no doubt also be a massive boost to morale for everyone who works and is cared for at our hospital."
Despite lockdown, Banksy has been finding ways to stay busy.
Last month, Banksy created a piece of art in his own house of rats causing havoc in his bathroom.