A 34-year-old man has been remanded in custody after the alleged murder of an elderly woman in a North Hobart supermarket yesterday.

Daryl Royston Wayne Cook, 34, appeared briefly in the Hobart Magistrates Court charged with murder and aggravated armed robbery.

It is alleged Cook attempted to rob the A&B Food Store on Elizabeth Street at about midday, stabbed the 68-year-old shopkeeper repeatedly and stole the cash draw from her till.

The victim, who had owned the store on the busy cafe strip for more than 10 years, received wounds to her neck and upper body.

She was treated at the scene by ambulance officers before being taken to Royal Hobart Hospital, where she died a short time later.

Cook appeared in court wearing a blue prison uniform and sat emotionless as the charges were read out.

He did not apply for bail and was remanded in custody.

Victim described as a 'lovely' woman

Police were on the scene until late into the night.

At about 11:00pm, police arrested and charged Cook at his Claremont home.

"The family is understandably very upset," Detective Inspector Ian Whish-Wilson from the Hobart CIB said.

This morning, police partially closed off Elizabeth Street in the vicinity of the incident as their investigations continued.

People took to social media to express their sorrow, describing the woman as "lovely" and "genuine" and "who loved a chat".

Police thanked the public for their help, after reaching out for assistance on social media.