An alert was raised at Chessington World of Adventures in Surrey just after 1400 IST, London Fire Brigade said.
The fire started before the attraction opened and no one was injured, the park said in a statement.
The flames were brought under control by about 1650 IST.
The blaze was near the zoo and all the animals had been moved to a safe place, the fire service said.
A statement posted on the park's website said: "Due to unforeseen circumstances, Chessington will be closed today."
"The theme park and zoo were closed at the time of this incident and therefore no guests were involved.
"All staff areas were immediately evacuated and all staff and animals are safe and well," the statement said.
The park said fire crews remained on site, and managers and the fire service would be investigating the blaze.
London Fire Brigade said about 40 firefighters attended the scene, where the fire affected a cafe and part of an attraction.
