Police were called to a home on Native Corners Rd at Campania, northeast of Hobart, about 3.30am on Monday after reports a person had been seriously injured by a car.
Emergency services later pronounced a 37-year-old woman dead at the scene.
A 38-year-old man from Campania was taken into custody at the property and is assisting police with their inquiries.
Tasmania Police Detective Acting Inspector Nicholas Bowden said the pair knew each other, but didn't confirm the nature of their relationship.
He said someone at the property called emergency services, but wouldn't elaborate on how many people were at the house at the time.
"Evidence located at the scene would suggest the female has been struck by a car," he said.
A white Holden Commodore, which was on the driveway near the front gate of the property, has been towed and will be further examined by crash and forensic officers.
Multiple marked police cars and an ambulance were at the scene on Monday as police combed sections of the property.
Detectives have urged anyone with information to contact Crime Stoppers.
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