Paramedics were called to a home at Native Corners Road in the Tasmanian wine region of Campania, north of Hobart, about 10am on Friday.
Upon arrival, first responders found a man in his 60s dead outside the home, while the body of the woman, also in her 60s, was found inside.
Detective Inspector David Gill said the deaths may have occurred shortly after calls were made to police and ambulance services by a family member of the couple who was not present.
"The male person has contacted a family member indicating an incident had occurred, and that family member then contacted Ambulance Tasmania," Det Insp Gill told reporters on Friday.
He said no one else is believed to have lived at the property and there was no ongoing threat to the community.
"The investigation, thus far, has indicated this is a family violence incident, and we are treating this as a murder-suicide," he said.
"The scene is extremely confronting to all the emergency services that attended the scene, and the images that they saw inside that residence will remain with them for their time."
Police have spoken to two close family members, whom Det Insp Gill praised for their bravery in helping with the investigation.
The couple were not known to police nor have there been any family violence concerns raised in the past.
The investigation is expected to run for several weeks as police gather evidence for a coroner.
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