Police were called to Frances Street, Woolwich, around 600 metres from the barracks, at 8.09pm on Thursday where they found the victim suffering from gunshot wounds.
Officers performed first aid before the London Ambulance Service and London's air ambulance arrived. The man was taken to an east London hospital with life-threatening injuries, the Met said.
Firearms officers and specialist crime detectives attended the scene. No arrests have been made and inquiries to identify a suspect are ongoing.
In a statement, the Met said: "Officers attended and found a man, aged in his 30s, suffering from gunshot wounds. They performed first aid until the London ambulance service and London's air ambulance arrived. The man was taken to an east London hospital with life-threatening injuries."
Anyone with information is asked to call police on 101, quoting CAD 6520/22OCT, or contact Crimestoppers anonymously on 0800 555 111 or online at crimestoppers-uk.org.