The body of Jean Campbell, 53, was discovered in Cranhill Park yesterday.
It is understood her husband went to look for her after she didn't come home and found her body.
Her dog was found in the park off Bellrock Street.
Police today released a picture of Mrs Campbell, who was last seen by a family member at about 5pm on Friday.
A post-mortem has taken place and police are now treating her death as murder.
Detective Chief Inspector Colin Carey said: "Extensive inquiries are continuing in the area to establish the exact circumstances surrounding the death and a motive for this murder.
"Detectives are trying to piece together Mrs Campbell's last movements.
"I would urge anyone who saw her between 5pm on Friday and Saturday morning to come forward.
"Her German Shepherd-type dog was with her in the park, so we are trying to establish when she left her house to take the dog for a walk."
Police have put on extra patrols in the area and say that anyone with any concerns should speak to officers.
Anyone with information is asked to contact police on 101 or Crimestoppers on 0800 555111.