The blaze, which began in a heater at a nearby gym, swiftly spread to the Corstorphine Youth Community Centre where the children were enjoying their October week break yesterday.
The building was soon well ablaze and the youngsters were escorted by staff to a nearby library before firefighters arrived. Nobody was hurt.
The fire service was still damping down the fire several hours after it was put out, but the building may have to be demolished.
It is thought to have started in a heater at the nearby Elite Fitness Studio, which was empty, shortly before 10am.
City of Edinburgh Council said it had assisted a family who lived next to the building. It was first opened in 1892 as Corstorphine Public Hall and is now a community hub. It had been extensively refurbished to include a new central heating system.