The body of the woman, who has not been named by the police, was found just before 11 am on Tuesday at a property on Victoria Street. A 57-year-old man was arrested on suspicion of murder at 2.50 pm.
In a short statement, the States police said the suspect remained in police custody while inquiries continue.
A spokeswoman said: ‘ Following the discovery of a suspicious death this morning, at 2.50 pm today a 57-year-old man was arrested on suspicion of murder. He remains in custody at PHQ and will be interviewed in due course.
‘This is the very early stages of a murder investigation – led by senior investigating officer Detective Chief Inspector Alison Fossey.
‘A UK Home Office pathologist will attend the Island to undertake a post mortem examination in order to help determine cause of death.
‘Specialist family liaison officers have been appointed to work in support of the family.
‘We are not yet in a position to be able to confirm the identity of the victim.’
The force say forensic work is likely to continue at the scene on Victoria Street which is near St Thomas’ Church. A major incident room has been set up at police HQ.
Anyone who heard or saw anything out of the ordinary in Victoria Street between Monday at 9 am and lunchtime on Tuesday is urged to contact the incident room on 612927 or call Crimestoppers on 0800555111