Police were approached by a man suffering from a stab injury to his face at around on Tuesday, 1 June in Hither Green Lane.
The victim, aged 23, has been taken to a south London hospital; his condition is currently being treated as life-threatening.
Officers are working to establish the circumstances and a crime scene is in place.
At this early stage there have been no arrests.
A Section 60 Order has been authorised in Lewisham from 7.50pm until 7am on Wednesday, 2 June.
Anyone who witnessed the incident or who has information that could assist police should call 1901 ref CAD 7106/1 June.
