The man in his 30’s was first seen standing on the roof of the supermarket on Asda Supermarket at around 11am on Friday morning.
A Met Police spokesman said: “Police were called at 10:36hrs on Friday, 11 May to the store in Bexleyheath, by the staff and a number of concerned members of the public following concerns for the safety of a man who had scaled the roof of an Asda supermarket.
“The man who is from the local is armed with a knife and had made threats to harm himself before jumping from the building.
Eyewitnesses earlier claimed he was threatening to jump off the roof and was holding a knife.
It is understood that the man has since jumped or fallen from the roof. He is being treated by LAS and will be taken to hospital.”
The London Ambulance Service and the London Fire Brigade attended the scene, as well as the air ambulance, which landing on a netball court in a nearby school field.