Mrs Walker, aged 86, and her 88-year-old husband Kenneth were found at their home on Station Road by a concerned neighbour at 9am on Saturday.
Freda was pronounced dead at the scene, while Ken, a serving member of Shirebrook Town Council and former Bolsover councillor, was rushed to hospital, where he remains in a critical condition with life-threatening injuries.
Derbyshire Police said the 33-year-old man was arrested in Warsop on suspicion of the murder of Mrs Walker and the attempted murder of her husband.
He remains in police custody at this time.
Since Saturday, detectives have been trawling CCTV and conducting house-to-house enquiries to find those responsible in the days since.
Assistant Chief Constable Dave Kirby, of Derbyshire Police, said: “Today’s arrest is clearly a significant breakthrough in the case.
“It comes from a lot of help and support from this community, and I would just like to say thank you to everyone who has helped us so far.
“That request still remains – so if you were on that street, either on foot or in a car, then please contact us as soon as possible.
“Yes, we have made an arrest, but of course, the investigation carries on, so we're always looking to add to the information that we've got.
“One of the leading lines of inquiry is it may have been a burglary and that remains a leading line of inquiry.
“The man was arrested in the early hours and, as you would expect, there will be interviews and so on, and if we can give any more information about motive then we will do, but at this time we can't be conclusive.
“We can't rule out the involvement of anybody else, but at the moment we are focusing our inquiries on this particular man we've arrested.
"As soon as we can update, particularly if the community are worried about any potential further risk to them about whether there might be somebody else, then we will give that update.
Anyone who may be able to help detectives with their enquiries is asked to contact Derbyshire police on 101, quoting reference 240-150122.