Eleven firefighting appliances and career and volunteer firefighters attended the scene on Wednesday evening.
It took them 45 minutes to extinguish the fire in three laundry bins and two teams cut a hole in the roof to help ventilate the room.
Most of the damage was due to smoke.
The fire was contained within the laundry room.
A Department of Corrective Services spokesman said very warm linen tightly packed in the clothing bins began to smoulder.
The Department of Fire and Emergency Services attended, and the WA Police Arson Squad found the fire was an accident.
Meanwhile, Corrective Services Minister Joe Francis conducted a surprise inspection of recently damaged cells at Hakea Prison in Canning Vale, using his powers under the Prisons Act, after learning of the damage 10 days after it occurred.
The damaged cells were in the section set up to house juveniles from Banksia Hill Detention Centre after rioting detainees damaged that Canning Vale facility earlier this year.
A Department of Corrective Services spokesman confirmed on Thursday that Hakea Juvenile Detention Centre detainees damaged four cells, in four separate incidents, on three different dates.
‘The damage was varied over the four cells but included damaged shelving, toilets and shower screens and observation windows,’ he said.
Repairs will cost around $7500.