The 32-year-old man, believed to be a detainee from Turkey, was found with serious injuries just before midnight on Wednesday.
He was rushed to Northam Hospital where he later died, West Australian police said in a brief statement.
Homicide detectives are investigating the incident and two people are assisting police with inquiries.
The Refugee Action Coalition said it was understood the man had been stabbed during an altercation with another detainee.
They claimed it had taken about an hour for an ambulance to attend the facility.
A video clip released by the group appeared to show the man receiving CPR and being loaded onto a stretcher by paramedics.
A small fire was also lit within the compound during the disturbance.
The man had been in held in Yongah Hill for about three years, having signed to return to Turkey around a year ago, the Refugee Action Coalition said.
Spokesman Ian Rintoul claimed it was the second stabbing incident at the facility in as many days.
"This tragic death must result in a full inquiry into immigration detention. This man should not have been in immigration detention," he said in a statement.
"It is common for detainees to be held for years even after they have signed to returned to their countries. The conditions in immigration detention are worse than jail, with no oversight."
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