The animal parts were discovered by a family visiting the grave of a recently deceased relative at Rockingham Regional Memorial Park at Baldivis, south of the Western Australian capital of Perth, on Monday.
"The effort that was put into it, the hate – it just beggars belief," one relative, a woman identified only as Mira, told radio station 6PR.
"For any dead animal to be put near your relatives is offensive."
The remains were spotted under the Muslim sign at the cemetery and were immediately removed.
"We take these isolated incidents seriously and Rockingham detectives will thoroughly investigate the circumstances surrounding the incident," a spokesperson for Western Australian police told AFP on Wednesday.
The cemetery said the gruesome discovery was the first of its kind at the memorial park.
The incident comes during the Muslim holy month of Ramadan when the faithful around the world fast from dawn to dusk.
Iqbal Samnakay, chairperson of Perth's Muslim Social and Sports Association, said the desecration of any burial site, Muslim or not, was offensive.
"We all expect burial sites to be kept in order and not to be desecrated," he told the WA Today website.
"As Muslims we are not meant to eat pigs, but that doesn't mean we should not respect them for what they are," he added of the animals.
Samnakay said whoever left the carcasses at the cemetery should be forgiven as it was "month of forgiveness" during Ramadan. – AFP