63-year-old Gurmail Singh had sustained head injuries during the robbery by four teenagers at around 8.30 pm on Saturday night, Feb 20.
The robbery at Cowcliffe Convenience Store was witnessed by a group of six people, who heard a commotion at the shop and went to help.
However, they were unable to prevent the gang of robbers from leaving.
Detective superintendent David Pervin said, "Singh was a well-known and popular local businessman who had been in this area many years. I appeal for anyone with information to contact us as a matter of urgency."
Singh was admitted to Huddersfield Royal Infirmary and he died at 3.30 am on Sunday morning, Feb 21.
A post-mortem will be held on Monday, Feb 22, to confirm the cause of the death, the police said.