The blaze was reported in the cellar of theatre, shortly before 3,30 this morning, in an area used to store batteries.
West Yorkshire Fire and Rescue Service brought in two pumps, ventilation fans and six sets of breathing apparatus. Three thermal image cameras were used to locate the seat of the blaze.
A fire spokesman said the building was heavily smoke logged, with some smoke in the main auditorium.
The theatre is expected to open as usual for this afternoon’s matinee performance of Joseph and the Amazing Technicolor Dreamcoat, starring X-Factor winner Joe McElderry.