The body of Jean Campbell, 53, was discovered in Cranhill Park in Glasgow's east end on Saturday morning.
Her German Shepherd-type dog was also found in the park, off Bellrock Street.
Mrs Campbell was last seen at around 5pm on Friday.
Police Scotland are treating her death as murder following a post-mortem examination.
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.
''Detectives are currently trying to piece together Mrs Campbell's last movements. She was last seen by a family member around 5pm on Friday night, so I would urge anyone who saw her between then 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.
''I would also like to reassure the local people that there are extra police patrols in the area, and anyone with any concerns should speak to officers.''
Anyone with information is asked to contact Police Scotland on 101 or Crimestoppers on 0800 555 111.