The 33-year-old man was arrested in Church Warsop, Nottinghamshire, on suspicion of the murder of Freda, 86, and the attempted murder of her husband Ken, 88.
The suspect remains in police custody at this time.
Freda and Ken were found at their home in Station Road, Langwith Junction, by a concerned neighbour at 9am on Saturday morning.
Freda was pronounced dead at the scene while Ken was rushed to hospital where he remains in a critical condition with life-threatening injuries.
Since Saturday, detectives have been trawling CCTV and conducting house-to-house enquiries to find those responsible in the days since.
Investigations are continuing and anyone with any information which could help detectives should contact Derbyshire Constabulary as soon as possible.