The final bell for Hamilton Senior High School rang on Thursday, and the building was set to officially close on Friday.
However police say an unknown offender gained entry to the building on Purvis Street in the early hours of Friday morning and set fire to a number of bins inside the school.
While there was no structural damage to the building, the damage cost is estimated at around $5000.
Police spokeswoman Susan Usher said the fire was being treated as deliberate.
The investigation comes just days after vandals trashed another Perth school.
Around 25 windows at Carlisle Primary School were broken during an attack on the weekend, and students in year one, two and three had to be shifted to the art room and library for their final week of classes.