People were evacuated and the city centre place of worship was forced to close following a fire in the organ blower room at lunchtime.
Firefighters from Ossett and Wakefield fire stations were called just before noon.
A statement issued by the Cathedral said: "The Cathedral suffered a small electrical fire in the organ blower room earlier today.
"Only a few people were in the CathedraI at the time and were immediately evacuated.
"It triggered the alarm system which is connected to the fire service, who were on the scene very quickly and secured the place.
"The investigation is ongoing and we do not expect the Cathedral to reopen until the end of the week as we try and reinstate power."
There will be no Evensong today or tomorrow and morning worship servcies tomorrow will be held in the Education Room.