The stand-off occurred at a residential address in Tilson Gardens in Clapham South, on Friday morning.
Police had tried to enter the property to help evict the man but, as they were doing so, a man was seen inside with what was thought to be handgun.
The firearm recovered at the scene is undergoing forensic tests, police said.
It is not yet clear if the object was a gun or a stun gun.
The 34-year-old man was shot outside the premises at about 16:45 BST, after armed response teams were called to the scene along with negotiators and ambulance crews.
He was arrested on suspicion of possession of a firearm with intent to cause fear of violence, police said.
The man was initially said to be in a critical condition but he is now described as stable.
The Independent Police Complaints Commission (IPCC) is investigating the incident.
In a statement it said: "IPCC investigators will continue to work at the scene today carrying out further forensic examinations, conducting house-to-house enquiries and a trawl for CCTV in the area.
"Investigators have also made contact with the man's family to explain our role and investigation."
A firearm has been found at the scene of a seven-hour police siege in south London in which a man was shot and seriously injured.