Police have advised residents living close to Liberton Primary School to keep their windows and doors closed as firefighters continue to battle the blaze.
Nine fire appliances - up to 50 firefighters - were called to the school shortly after 3:30pm on Wednesday after a fire broke out in one of the classrooms.
A fire service spokesman described the fire as "well developed" and there have been reports from eye-witnesses of the roof caving in.
The school will be closed for the rest of the week and parents will be told next week about contingency plans before pupils go back after the half term on February 17th.
A video shared on social media shows flames coming out of a first floor window.
Police in Edinburgh have his evening issues a statement which says the roads around the school are currently closed and "will be for some considerable time." Motorists are being advised to avoid the area.
The statement also said: "As a precaution at this time residents in the immediate area of the school and being advised to keep windows to their homes closed meantime."
Inspector Scott Casey said: "Officers were alerted to the fire at around 3.37pm this afternoon. There are no reports of any injuries. The fire is being tackled by the Scottish Fire and Rescue Service and we are assisting with traffic control at this time.
"It is expected that emergency services will be in attendance for most of the night and people are asked to avoid this area where possible."
Education convener, councillor Ian Perry, described it as a "major fire" which has caused "significant damage" to a large part of the school.