The "bemusement park" at a derelict seaside lido in Weston-super-Mare attracted thousands of visitors when it opened last summer.
Other awards nominees include electronica band Years and Years and the BBC Two adaptation of Wolf Hall.
The winners will be announced at a ceremony, hosted by Lord Melvyn Bragg, at London's Savoy Hotel on 5 June.
Now celebrating their 20th anniversary, the awards honour "the very best of British culture and achievement".
Banksy competes in the visual art category against Cornelia Parker for Magna Carta (An Embroidery) at The British Library and Lynette Yiadom-Boakye: Verses After Dusk at the Serpentine Gallery.
Historical drama Wolf Hall is joined in the TV drama category alongside Channel 4's Humans and Doctor Foster (BBC One).
In the pop category, Benjamin Clementine, Years and Years, and Sleaford Mods go head to head.
The film category features Ex Machina, 45 Years and Brooklyn, while the theatre contenders are Oresteia, People, Places and Things and Hangmen.
Lord Bragg said the South Bank Sky Arts Awards were a "freeze-frame on a unique moment in British cultural history".
He added: "This is the 20th of these annual awards and a ripple through the records shows an extraordinary tapestry of talent, ever-changing but always the same in its high quality."
2016 FULL LIST OF NOMINEES

The X Factor's 13th series began in August with 8.5 million viewers - four million fewer than 2010's launch show.
The Voice will move from the BBC to ITV next year, also on a three-year deal.
But the broadcaster has agreed a deal with Simon Cowell for both The X Factor and Britain's Got Talent to continue on ITV until at least 2019.
Cowell said: "I want to thank ITV for continuing to be fantastic partners. I'm delighted for the shows and, in particular, for all the talented people who work on them with us."
Cowell may not appear as a judge on both programmes, though - under the new deal he is only committed to judging one of the two series per year.
ITV is currently negotiating with Ant and Dec to remain as hosts of Britain's Got Talent for the next three years. Dermot O'Leary's current contract means he will keep presenting The X Factor until at least 2019.
ITV's director of television Kevin Lygo said Britain's Got Talent and The X Factor were both "big, brilliant, wonderful shows" that would form "an important part of our schedule" for the next three years.
"They are defining shows for us, ones that we are very proud to have as part of our entertainment slate, and they continue year after year, for months at a time, to be amongst the most popular and hugely entertaining formats on television," he said.
Elusive artist Banksy has landed a South Bank Sky Arts Award nomination for his Dismaland theme park.
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The X Factor is to stay on ITV for at least the next three years, despite declining viewing figures and the arrival of The Voice to the channel.