The body of Angela Humphrey, 48, was discovered by relatives in her flat in Quarrywood Avenue, in the Barmulloch area of Glasgow, at around 4.40pm last Wednesday.
Police said she lived alone and had not been seen since the previous Friday in Balbeggie Street in the city.
Relatives who had become concerned at a lack of contact with Ms Humphrey went to her flat and discovered her body.
A 55-year-old man was arrested yesterday morning by police over the death and is due to appear at Glasgow Sheriff Court later.
A force spokeswoman said: "Following an intelligence led operation, a 55-year-old man was arrested and is currently detained in police custody in connection with the death of Angela Humphrey, whose body was found in Quarrywood Avenue on Wednesday February 26."