Firefighters attended the scene shortly before 8pm on Tuesday evening and the fire was extinguished within minutes.
The attraction, which opened last year, has and will remain closed until the cause of the blaze can be determined.
A spokesman for Thorpe Park said: “The attraction will remain closed until the investigation is complete and while we assess the extent of the damage.
“It will re-open when we have brought the maze back to full operating standards and had it passed through the relevant Health and Safety inspections.”
The rest of the park remains open as usual.