The woman has not been named as family members are still being informed.
Detective Inspector David Tassie, from Hamilton CID, said: "From extensive inquires which have taken place so far I would like to reassure the local community that I do not believe this was a random attack.
"A team of detectives has been assigned to this investigation and an incident room has been set up.
"Door-to-door inquiries are also being carried out and forensic examinations are continuing to gather any information which can help our investigation. Extra uniform patrols are in the area and I would urge anyone who has any concerns to speak to an officer.
"I would also appeal to anyone who heard a disturbance or noticed anything unusual in Old Coach Road in the past few days to contact the incident room on 01355 564016."