Met Police officers were called to reports of a man with stab wounds at an address on Monson Road, New Cross, at 7.30pm on Saturday.
The force attended the scene with the London Ambulance Service and medics from the London Air Ambulance who provided emergency care.
Officers said the 26-year-old man died at the scene, and specialist officers are supporting his family.
Scotland Yard said another 26-year-old man was arrested on suspicion of murder a short time later. He remains in custody as of Sunday afternoon.
Read more from Sky News:
Murder suspect in fatal shooting of young mum being ‘protected’
Child vaccination rates are the lowest in more than a decade – why?
Detective Chief Inspector Lucie Card, who is leading the investigation, said: “Our thoughts are with the family and friends of the victim at this difficult time.
“I understand this incident will be concerning and we are carrying out a fast-paced and thorough investigation to establish the circumstances.
“I would encourage anyone who has not yet spoken to us.”
