The Royal Agricultural & Horticultural Society of SA (RA&HS) announced on Thursday that due to the rising Delta variant in New South Wales, Victoria and Queensland, they were forced to cancel the event.

They said SA Health had advised mass gathering events in the state had to be significantly limited in numbers for the foreseeable future, with a daily cap on attendance to the Royal Adelaide Show being less than 10,000 people.

"In a regular year, the Royal Adelaide Show can attract over 50,000 members of the public per day and, additionally, have up to 10,000 people working or competing at the Show each day," a statement on the Royal Adelaide Show's website said.

The Royal Adelaide Show was scheduled to run from Saturday, September 4 to Sunday, September 12.

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Organisers said it was with "great sadness" that they had to cancel yet again.

"In the Society's 182-year history there have only been five reasons for the Show not being held, namely, the Victorian Gold Rush in 1852, WWI, the 1919 Spanish Flu pandemic, WWII and now the ongoing COVID-19 pandemic," they said.

"As you can appreciate, unravelling Show preparations this close to the scheduled opening of the event is a significant undertaking.

"The RA&HS cordially asks that all involved in the Show be patient whilst the Society administration methodically works this through."

Premier Steven Marshall said at a press conference on Thursday the decision was made with "huge regret".

"It's with huge regret that the society will be announcing that the Royal Adelaide Show will not be going ahead" Mr Marshall said.

"Crowd numbers are one issue but also many of the attractions, the rides come in from interstate."

Ticket holders can receive a full refund from where they purchased a ticket.