She was treated at the scene by ambulance officers before being taken to Royal Hobart Hospital, where she died a short time later.
Police have established a crime scene on the busy Elizabeth Street cafe strip, and are treating the investigation as a murder.
Detective Inspector Ian Whish-Wilson from the Hobart CIB said robbery was a probable motive.
“It is believed that a metal cash draw has been taken from the scene,” he said.
“We believe at the moment that it’s probably a hold-up gone wrong.
“We’re calling on information from any person, any member of the public, who may have witnessed the incident or has any knowledge.
“The family is understandably very upset.”
Police have interviewed staff from neighbouring shops and cafes who were shaken up by the incident.
A command bus has been set up at the scene, with forensic officers expected to be on the scene into Saturday night.