Karshak was playing on the scaffolding at a refurbishment scheme on the Kingsmead Estate in Hackney, east London.
Galliford Hodgson pleaded guilty to breaching a section of the Health and Safety at Work Etc Act 1974. The prosecution was brought by the Health and Safety Executive.
A court found that the accident could have been prevented had fencing been in place to keep people off the site.
Philip White, head of operations for London, East and South-east at the HSE construction division, said: “This case emphasises that all those involved with refurbishment of occupied premises, including principal contractors and clients, need to think carefully about how members of the public, children in particular, might be harmed by construction work.”