Firefighters managed to catch two teenagers fleeing from the new Millwood Special School site, in Abden Street, Radcliffe.
ISG project manager Paul Higgins said part of the building would now have to be taken down and rebuilt which could push back the November completion date.
The fire was started in a doorway and spread to cladding leaving a classroom badly damaged by the blaze.
Watch commander, Gary Stredder, told the Bury Times: “A doorway and cladding were well alight.
“The fire was extinguished within 15 minutes. This incident is what we call a good stop. Had the fire been left for another few minutes, it would have spread to other parts of the development.”
Police confirmed that two 18-year-olds had been arrested on suspicion of burglary and arson.
The new school will be single-storey, with a main hub and separate areas for children with different educational needs, including 14 classrooms, a hydrotherapy room, staff areas, and a library.
ISG has been on site since last October
Higgins said: “The damage to that part of the building means it will need taking down and rebuilding. We are looking at the implications that will have on the completion date.
“We have now increased security on the site to combat people breaking in and causing damage in future.”