Eye-witnesses told local paper The National that a wall collapsed after being hit by a crane.
Four men were taken from the site to the Royal Infirmary of Edinburgh and their condition is currently unknown.
A Scottish Ambulance Service spokesperson said: “We received a call at 11:01 to attend an incident on Rillbank Crescent, Edinburgh.
“Four ambulances, two special operations response teams (SORT), and a critical care paramedic were dispatched to the scene.
“Four patients were transported to the Royal Infirmary of Edinburgh.”