The woman, named locally as Freda Walker, died at her home in Langwith Junction in Derbyshire.
The 88-year-old man, thought to be her husband Ken Walker, was taken to hospital for treatment.
Paramedics called police to the house in Station Road at 9.30am on Saturday.
Derbyshire Police said the woman was aged 88 but a friend said that she was 85.
The family of the couple have been made aware and are being supported, police said.
Ch Supt Hayley Barnett has asked anyone with information about what happened to contact police “as a matter of urgency”.
“This is an understandably shocking incident for the community in Langwith Junction and our thoughts are with everyone affected, in particular those family and friends of the man and woman,” she said.
Police are still at the scene, and Ch Supt Barnett said residents in and around Station Road will see “an increased police presence in the coming days”.
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