Police were called by paramedics at 9.30am on Saturday to reports that a man and a woman had been found with serious injuries at a house in Station Road, Langwith Junction.
The 86-year-old woman was pronounced dead at the scene while the man, aged 88, is being treated at hospital for life-threatening injuries.
The family of the couple have been made aware and are being supported by specialist officers.
Officers remain at the scene and there will be a significant police presence for some time.
Divisional Commander, Chief Superintendent Hayley Barnett, said: “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.
“Residents in and around Station Road will see an increased police presence in the coming days and I want to reassure all those in the area that all force resources, as well as regional colleagues from the EMSOU Major Crime team, are working to understand the full circumstances of this incident.
“I would urge anyone who has any information about the incident to contact the force, in confidence, as a matter of urgency.”
Anyone who may be able to help detectives with their enquiries is asked to contact Derbyshire police on 101 or anonymously contact the independent charity Crimestoppers, on 0800 555 111 or by visiting www.crimestoppers-uk.org.