Police were called at 7.54pm to reports of a stabbing in Milford Towers, Catford SE6.
Officers responded with LAS and found a man, believed in his 30s, with a stab injury.
He was taken by ambulance to a South London hospital; we await an assessment of his condition.
Officers are working to establish what happened. There have been no arrests at this stage.
A number of scenes are in place in the block.
Anyone who has information or material that could help police should call 101 ref CAD 7406/10 Jul.