Bropho, a 40-year-old Indigenous man with an intellectual disability, was found dead in his cell on Thursday morning.
It's believed he had been bashed by other prisoners.
West Australian police confirmed homicide squad detectives were investigating Bropho's death.
"The death is being treated as suspicious and a number of male prisoners are assisting detectives with their inquiries," a police spokeswoman said.
Bropho had been due to be sentenced in the District Court next week after pleading guilty to abusing a nine-year-old girl he lured back to his Doubleview home from a nearby park.
His lawyer Clint Hampson confirmed on Thursday that prison authorities had informed him of his client's death.
WA's Department of Justice said a prisoner had been found unresponsive in his cell just after 8am.
"Prison staff provided first aid and paramedics attended but the man was unable to be revived," a spokeswoman said.
"The circumstances surrounding the death will be subject to a police investigation.
"The prison is assisting the investigation and two units have been placed in lockdown to assist police.
"WA Police will provide a report to the state coroner."
Three St John WA crews attended the facility in response to the incident.
Bropho had been living under the supervision of an NDIS carer in July last year when he committed the sexual offences that led to his imprisonment.
WA Prison Officers Union secretary Andy Smith said tensions had been rising at Hakea for several months, with overcrowding and understaffing "frequently reported".
"In response, our officers have been forced to make adjustments to procedures in order to run the prison," he said.
"Today's traumatic incident unfortunately demonstrates the risks prison officers face while doing their jobs in a difficult environment."
Youth custodial officers have meanwhile walked off the job at the troubled Banksia Hill juvenile detention centre.
CPSU/CSA branch secretary Rikki Hendon said negotiations had broken down with the state government after almost a year of bargaining on a new pay deal.
Conditions at Banksia Hill have been described as dangerous, with staff shortages contributing to repeated lockdowns.
A youth custodial officer last month suffered a suspected fractured skull after being hit by objects allegedly thrown by detainees who scaled fences and rooftops.
"It is time the government started treating its frontline workers at Banksia Hill with the respect they deserve and stop avoiding their responsibility to workplace health and safety," Ms Hendon said.
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