The child was in the Hugo Boss store in the Bicester Outlet shopping village in Oxfordshire on Tuesday evening when the shop fitting fell causing severe head injuries.
He was taken to the John Radcliffe Hospital in Oxford where he died in the early hours of yesterday morning.
Police are investigating the death and have appealed for witnesses to the incident to come forward.
A Hugo Boss spokesman said: “Everyone at Hugo Boss is devastated by this tragic accident and we would like to extend our deepest condolences and sympathies to his family. All of our thoughts are with them at this time.”
The shop will remain closed until further notice.
Investigating officer Detective Inspector Steve Duffy said: “Our thoughts are with the family at this time.
“We are currently investigating the circumstances of this boy’s death and we would ask anyone who was in the Hugo Boss store at around that time [8:30pm] on Tuesday to please contact us as a matter of urgency.”
The Bicester shopping village has around 130 luxury fashion and homeware stores and is one of the most popular out-of-town discount outlet villages in the UK.
The Health and Safety Executive said that it was not involved in the investigation into the death of the boy as shops are the responsibility of local authority environment health departments.