The body of Jean Campbell, 53, was discovered in Cranhill Park in Glasgow's east end on Saturday morning. Her dog was also found in the park off Bellrock Street.
Mrs Campbell was last seen at around 5pm on Friday.
A post-mortem examination has taken place and Police Scotland are now treating her death as murder.
Detective Chief Inspector Colin Carey said: "Extensive inquiries are ongoing in the local area to establish the exact circumstances surrounding the death and a motive for this murder.
"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.
"I would also like to reassure the local people there are extra police patrols in the area, and anyone with any concerns should speak to officers."
Anyone with information is asked to contact 101 or Crimestoppers on 0800 555 111.