Emergency services were called to Kaimes School on Tuesday and paramedics treated the 17-year-old boy, but he was pronounced dead at the scene.
Police Scotland said there are no suspicious circumstances surrounding his death, and a report will be submitted to the procurator fiscal.
Amanda Hatton, executive director of education and children's services at Edinburgh City Council said: "I am absolutely saddened to hear this tragic news and my immediate thoughts are with the family.
"My heartfelt sympathies go out to the school community and everyone who has been affected. Support is being offered to any pupils or staff who may require it."
The Lasswade Road school, which is for pupils who are on the autistic spectrum, was closed on Wednesday.
A Police Scotland spokesman said: "Around 11.30am on Tuesday January 25, police responded to a concern for person call at a school on Lasswade Road, Edinburgh.
"Medical assistance was provided by paramedics to a 17-year-old boy, however he died at the scene.
"There are no suspicious circumstances surrounding his death and a report will be submitted to the procurator fiscal."