Police closed a section of West Blackhall Street around 9.30am on Sunday when the victim was injured in the flat.
Emergency services vehicles, including police cars and ambulances, were at the scene for some time after the incident.
Eyewitnesses saw the victim being taken to an ambulance.
Traffic was diverted from the incident, causing congestion in other parts of the city.
Police have admitted that a 55-year-old man has been charged in connection with the alleged attack.
A policeman Scotland The spokesman said: “Police were notified around 9.25am that a man had been injured inside a property in the West Blackhall Street area of Greenwich.
The man was taken to Queen Elizabeth University Hospital for treatment and a 55-year-old man has been charged in connection with the incident.