The broke out on Dunkery Road yesterday (July 17) and a large number of emergency services were at the scene, including 15 firefighters and three fire engines.
London Ambulance Service was also in attendance and treated the man at the scene for heat burns.
The incident was first reported at 12.16pm and was fully under control by 1.05pm and crews from Eltham, Sidcup, and Lee Green fire stations responded to the fire.
Investigations are underway to confirm the cause of the blaze, though initial police reports suggest the incident was accidental and not a case of arson.
The man was later taken to hospital as a precaution.
A spokesperson for London Fire Brigade said: “Three fire engines and around 15 firefighters tackled a shed fire on Dunkery Road in Bromley.
“Four sheds belonging to adjacent properties were destroyed by fire, as was fencing between the properties.
“One adult man suffering heat burns was treated on-scene by London Ambulance Service.
“The Brigade was called at 1216 and the fire was under control by 1305.
“Crews from Eltham, Sidcup and Lee Green fire stations attended the scene.
“The cause of the fire is under investigation.”
Bromley MPS tweeted: “Yesterday there was a significant emergency services presence in Dunkery Road, SE9 and road closures were implemented.
“This was due to a fire at the location.
“At this time it is believed to be accidental and is not suspected to be arson.
“One resident was taken to hospital, just as a precaution.”