Police were called to Deerhurst House, on Haymerle Road, in Peckham, on Friday afternoon.
The man, aged in his 20s, was treated by paramedics but died at the scene. His family have been told and a post-mortem examination will be held on Sunday.
Scotland Yard said no arrests had been made and appealed for witnesses to contact the force.
A man has been stabbed to death outside a block of flats in south London.