Officers were called to an address at Cumlodden Drive in Maryhill at around 5.24pm on Tuesday.
They found the body of a 54-year-old woman, who has now been identified as Jacqueline Grant.
Relatives have been made aware of Ms Grant’s death.
Police were initially treating the incident as a suspicious death but are now treating it as murder after a post mortem was carried out.
Detective Chief Inspector Stuart Grainger said: “Jacqueline died as a result of a brutal attack in her home and her family are devastated by what has happened.
“We have a dedicated team of officers dealing with the case supported by local officers and specialist resources including forensic and search trained officers, carrying out a detailed search of her home and the local area.
“Officers have also been checking CCTV in and around the flats and in nearby streets and have been carrying out local enquiries, speaking to neighbours, residents and businesses to try to glean as much information as they can.
“However, we are still keen to hear from anyone who was in the area either later in the evening or night of Monday April 5 or the early hours and into the morning of Tuesday April 6.
“If you have not yet spoken to police, and have information, no matter how insignificant it may seem to you, about the murder, then please contact Police Scotland via 101, quoting reference number 2388 of April 6, 2021.”
Crimestoppers can also be contacted anonymously on 0800 555 111, and police have also set up an online portal to encourage members of public to submit information.