The Jamaican artist who created the installation claims to have been the first person to reveal Banksy's identity, by photographing him in 2004.
Peter Dean Rickards bought the wall which featured the mural from a bar in Kingston and intentionally smashed it.
The exhibition, at the New Art Exchange, celebrates 50 years of Jamaican independence.
Curator of the exhibition Rachael Barrett said: "Most Jamaican people didn't really understand why it [the mural] would be a valuable work of art.
"The artist, Peter Dean [Rickards], is questioning this fake sense of value and obsession with celebrity we've got."
The mural was a version of Banksy's Balloon Girl. Mr Rickards paid about Â£1,500 for the wall "in cash and rum", Ms Barrett said.
Banksy is thought to have painted it in Jamaica's capital in 2004.
Mr Rickards claims to have photographed Banksy at work while he was in Kingston.
In 2008 the Mail on Sunday claimed to have worked out Banksy's identity from one of the photos, and named him as former public school pupil Robin Gunningham.
Also in 2008, it was reported that Mr Rickards had allowed a dog to defecate on the artwork after he bought the wall.
A video of him removing the mural plays on loop alongside the installation in Nottingham.
The smashed wall is displayed in the corner of a room, which has been made to look like the garage in which it was stored for several years after being cut down.
Mr Rickards is quoted in the exhibition notes as saying: "That was done by a guy in the UK named Banksy.
"The white people love him there and he sells stuff like that for thousands of pounds. Lets cut it down!"
The exhibition, called I Is AnOther, is on until 8 December.
A defaced mural by the graffiti artist Banksy has resurfaced in an exhibition at an art gallery in Nottingham.