The inmate scaled the building at 10am today.
Neighbours said they had heard him asking for a McDonald’s.
Fire crews, police and ambulances have all been called to the incident, which a Scottish Prison Service spokesman said was “standard procedure”.
He said: “The SPS can confirm a male prisoner has climbed onto the roof of a building within HMP Edinburgh. Trained staff are are dealing with him and they are endeavouring to bring the incident to a safe conclusion as quickly as possible.”