Officers were called to a house on Oak Crescent in Littleover, at around 7.15am this morning.
On arrival an injured woman was found and was pronounced deceased at the scene.
A 44-year-old man has been arrested on suspicion of murder and remains in police custody.
Officers remain in the area and a scene is in place.
No further information is available at this time.
Anyone with information that could assist enquiries is asked to contact us using the following methods, quoting incident number 225 of 6 February.
You can also anonymously contact the independent charity Crimestoppers, on 0800 555 111 or by visiting www.crimestoppers-uk.org.