Officers were called to a home in Gordon in Canberra's south for a welfare check after reports of a disturbance about 7.30am on Sunday.
They found the body of the woman inside her Togo Place home.
Detective Acting Superintendent Stephen Ladd said police arrested the woman's 86-year-old husband at a house about 10km northeast in Fadden.
The man remains in hospital under police guard and is being treated for a possible cardiac episode.
No charges have been laid.
"We are treating this as suspicious and treating it as a homicide investigation," Superintendent Ladd told reporters.
Police declined to detail the crime scene nor the woman's injuries, and said a post-mortem would determine the cause of death.
Superintendent Ladd said he didn't believe any other people were involved and the couple was not previously known to police.
"At this stage the husband is obviously helping us with our inquiries and due to that familial relationship, we are treating this as a family violence incident," he said.
"Incidents like this are tragic and my heartfelt sorrow goes out to the friends and family.
"If you think there are issues with mental or physical health, particularly as people get into their elder years, reach out and talk to someone and get the assistance they need to avoid situations like this."
Meanwhile, a 43-year-old man has also been arrested in relation to the death of a woman in Darwin.
Northern Territory Police said they received reports of an unresponsive woman at a home in Coconut Grove in the city's north about 12.30pm on Sunday.
A 36-year-old woman was declared dead at the scene.
A 43-year-old man presented himself to police at the residence and was arrested, NT Police said in a statement on Sunday.
He remains in custody.
The man and woman are believed to be known to one another.
A crime scene has been declared and investigations are ongoing.
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