Images show a silver car surrounded by police as a man lying in a pool of blood is treated for a gunshot wound.
Police said they received multiple 999 calls after locals spotted a man with a firearm.
Specialist firearms officers rushed to the scene where they found the suspect.
Scotland Yard said officers fired their weapons and the man was injured.
His injuries are not believed to be life threatening.
Gary Clarke, who has lived on a nearby estate for more than three decades, said: “I just heard the gun shot, I heard a ‘pop’ from my bedroom.
“Then four minutes later I heard the air ambulance, the police turned up. My daughter went over there and she said, ‘Someone has been shot on the bridge’.
“She was quite shocked and a bit shaken up. You don’t expect someone to do that it’s broad daylight – it’s quite shocking.”
Gemma Daly, 31, from Whitstable, but staying in Greenwich, said she heard some shouting and then “a big bang” which she believes was a gunshot.
She said she heard police sirens straight away, adding that the emergency services then started arriving.
“Police were attending to a man on the side of the bridge,” she said, adding that he was “clearly injured”.
“They removed his clothing”, she said, describing how “a lot of people” were working on the man before he was put on a stretcher.
Ms Daly said police “started to go around” a silver car, which was still on the bridge.
A Scotland Yard spokesman said: “He was treated at the scene before being taken to hospital.
“No other injuries have been reported. Significant cordons are in place. We ask members of the public to avoid the area.
“While the investigation is in its early stages, this incident is not believed to be terror related or that there is an ongoing threat to the wider public.”
A London Ambulance Service spokesperson said: “We sent a number of resources including an ambulance crew, an advanced paramedic, a motorcycle paramedic, a medic in a fast response car and an incident response officer, and we also dispatched medics from London’s Air Ambulance.
“We treated a man at the scene and took him as a priority to a major trauma centre.”
The Directorate of Professional Standards watchdog has been informed of the shooting.