Sidcup Family Golf in Sidcup Bypass has been closed for three days following the incident on Sunday (November 9) at 5.45pm.
It was previously reported that the boy, 5, was fighting for his life from the wall collapse.
A second child, a six-year-old girl was also injured and has since been discharged from hospital.
The venue has since confirmed that the boy has died.
A spokesperson for Sidcup Family Golf said: “We are deeply saddened to hear that the child injured on Sunday has tragically passed away.
“Our heartfelt condolences go out to the child’s family and loved ones at this incredibly difficult time.”
They added: “We are co-operating fully with the authorities as they continue their investigation and are providing every possible support to those affected by this tragedy.”
The Metropolitan Police is yet to comment.
It is understood that the two were at a birthday party held at the venue at the time of the incident.
Following the collapse, a spokesperson for the centre said its first priority was “ensuring they received immediate medical attention”.
An eyewitness also told the News Shopper that staff at the centre worked well in quickly looking after the injured children.
