Police were called to the building in Grosvenor Square in Mayfair, which is the centre of a £250 million renovation, after the tragedy yesterday afternoon.
The site of a former US naval headquarters is yards from the US Embassy. Officials from the Health and Safety Executive officials were at the scene.
Police said the man, believed to be in his 30s, was pronounced dead.
Officers asked members of the public to avoid the area, including anyone planning to go to a demonstration nearby at 6pm.
The force said: "Police are advising motorists and the public to avoid the Grosvenor Square area following a partial building collapse.
"Police were called at 3.45pm today, Monday April 14, to a building site on Grosvenor Square. Officers, London Ambulance Service, London's Air Ambulance and London Fire Brigade are in attendance.
"A man, believed to be in his early 30s, who was working on the site, was pronounced dead at the scene. At least one other person has been injured.
"The Health and Safety Executive has been informed. Road closures remain in place."
The workers' employers, McGee Construction, would not comment.