Officers were called to Newman Hospital after 4am on Wednesday where the woman was pronounced dead.
A man has been taken into custody, according to local publication the North West Telegraph.
A house close to the hospital has reportedly been cordoned off by police.
A statement from WA Police said homicide detectives are investigating the death.
The woman’s identity, age and cause of death have not been released at this stage.
Anyone with information is asked to contact Crime Stoppers on 1800 333 000 or by making a report at Crime Stoppers online.
– With AAP