The child was at the store at the Bicester Outlet shopping village in Pingle Drive last Tuesday evening when it is believed part of a shop fitting fell on him causing serious head injuries.
The boy was taken to the John Radcliffe hospital in Oxford where he died in the early hours yesterday, Thames Valley police 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 on Tuesday to please contact us as a matter of urgency," Investigating officer Detective Inspector Steve Duffy was quoted by 'The Guardian' as saying.
In a statement, Hugo Boss said the boy was injured after a mirror fell on him.
"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. Hugo Boss will assist the authorities in any way with an investigation into the accident," the statement said.
A company spokesman said the store would remain closed until further notice.
