The £40,000 machine was taken, along with another ride, after it was parked near to a service station in Fife.
Police said the determined thieves would have needed another vehicle fitted with towing equipment to take the ride from the site in Kinghorn last week.
The 18-foot trailer is easily identifiable with pink and blue colours and rides including Disney characters, several horses, a red bus, fire engine, car and dolphins.
Community sergeant Darren Stewart said: "This is quite an unusual theft concerning a high-value piece of showground equipment.
"For someone to steal the trailer would require a high-powered or large vehicle fitted with the necessary towing equipment.
"I am asking for anyone who may have witnessed this theft or to anyone connected with this industry who may have been offered the ride for sale to contact the police in confidence."