A man she knew is in custody and two teens who witnessed the alleged killing have been left "significantly distressed", police say.
Emergency services were called to a home in Binalong Road, Mornington, about 1.30pm.
Police said they received reported a woman had been injured with a knife and found here in a serious condition, with upper-body injuries.
The 52-year-old died shortly after arriving at Royal Hobart Hospital.
Police said a 60-year-old Hobart man was taken into custody without incident at the scene.
"Two other people – aged in their teens – were present at the time of the incident," police said, in a statement.
"The two teenagers were not physically injured but of course they are significantly distressed by this incident."
Police said all violence was unacceptable and family violence should not be tolerated.
"Any incident like this is confronting and distressing to all involved from loved ones to the community, to emergency services who attended," police said.
"When children are involved, it certainly does have an impact on our officers. Wellbeing support is provided to officers affected by incidents."
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