Six fire engines and around 40 firefighters were called to a flat fire on Bramlands Close in Battersea.
Part of a three-roomed flat on the 16th floor of the building was damaged by fire. One man was treated on scene.
Station Commander Clive Robinson, who was at the scene, said: "Crews worked quickly to bring the fire under control, which was located in the kitchen of a flat at a residential block.
"One man left the affected flat before the Brigade arrived, who was treated on scene."
The Brigade's Fire Investigators believe the fire was accidental and caused by cooking.
The Brigade was called at 1522 and the fire was under control by 1617. Fire crews from Fulham, Chelsea, Brixton, Lambeth, Kensington and surrounding fire stations attended the scene.