The emergency services were called to Penfold House on Wrottesley Road around 3pm yesterday (May 7).
A 20-year-old was rushed to hospital for his stab wound, described by paramedics as “serious”.
Police have also been contacted for details of the victim’s condition.
There have been no arrests and a police investigation has been launched.
A London Ambulance Service spokesperson said: “We were called at 3.03pm yesterday (7 May) to reports of a stabbing in Wrottesley Road, Plumstead.
“We sent an ambulance crew, a paramedic in fast response car and an incident response officer to the scene.
“The first paramedic arrived in less than six minutes.
“We treated one patient for a serious injury and took him to a major trauma centre as a priority.”
A Met Police spokesperson said: “On Wednesday, 7 May police were called at 14:59hrs to Penfold House, SE18 following reports of a stabbing.
“Met officers attended the scene alongside paramedics from the London Ambulance Service who treated a 20-year-old man for a stab injury to his hand before taking him to hospital.
“We await an update on his condition.
“At this early stage, no arrests have been made, and an investigation has been launched into the circumstances.
“If you saw, or have any information that may assist then please call police on 101 stating CAD4296/07MAY or call Crimestoppers on 0800 555 111.”