The 45-year-old's body was discovered last Wednesday at a flat in Dobbie's Loan Place, Townhead.
Her body was found after concerns were raised she had not been seen for some time.
Officers forced their way into the flat and found her body inside.
She is believed to have lain dead for up to three weeks.
The last sighting of her was at Woodside Health Centre on October 9.
A murder inquiry was launched following a post-mortem.
Police believe she was the victim of an unprovoked attack.
The major investigations team is carrying out door-to-door inquiries and speaking to the woman's neighbours, as well as reviewing CCTV film.
Anyone with information is asked to call police on 101 or Crimestoppers anonymously on 0800 555111.
Meanwhile, a man was due to appear at Glasgow Sheriff Court today following an alleged rape in a Gorbals car park last week.
The 24-year-old was arrested by officers investigating an incident involving a 35-year-old woman in Bridge Street, who is said to have been attacked after attending a fancy dress party.