The body of Angela Humphrey was found in a house in Quarrywood Avenue, Barmulloch, in the north-east of the city, on Wednesday afternoon.
Police said a post mortem had been held and her death was being treated as murder.
Ms Humphrey lived alone and her family have been informed of her death.
Detective Inspector Allan Burton said: "Angela lived alone and had not been seen since last Friday in Balbeggie Street, Sandyhills, Glasgow.
"Yesterday, relatives who had not seen her for a couple of days and concerned that she had not been in touch with them, discovered her body within her home.
"We are obviously very keen to establish her whereabouts between last Friday and when she was found yesterday afternoon. Officers are currently carrying out door to door enquiries in the area and checking local CCTV to establish her last movements.
"Angela is described as white, approximately 5 ft 4, of medium build, with shoulder length black hair. She was wearing black framed glasses, black trousers, black and white trainers, cream and black three quarter length hooded 'Parka' type coat.
"She is known to frequent Springburn Shopping Centre and a tanning salon in Springburn Way, Glasgow.
"Anyone with information can contact officers on the non emergency number 101 or call Crimestoppers on 0800 555 111 where details can be given in confidence.