Fatou Saine, 33, was attacked where she worked last week in McColls in Glasgow's St Enoch Square.
Police were called to the store at around 11.55am, where they found the dead worker.
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Hide AdThe shop was cordoned off while a forensic team examined the scene.
Another member of staff and some customers were in the shop at the time of the disturbance but they were not injured and did not need hospital treatment.
A 43-year-old man has been arrested and is being held in police custody.
A report will be sent to the procurator fiscal.