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.
鈥淭he effort that was put into it, the hate 鈥� it just beggars belief,鈥� one relative, a woman identified only as Mira, told radio station 6PR.
鈥淔or any dead animal to be put near your relatives is offensive.鈥�
The remains were spotted under the Muslim sign at the cemetery and were immediately removed.
鈥淲e take these isolated incidents seriously and Rockingham detectives will thoroughly investigate the circumstances surrounding the incident,鈥� a spokeswoman 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, chairman of Perth鈥檚 Muslim Social and Sports Association, said the desecration of any burial site, Muslim or not, was offensive.
鈥淲e all expect burial sites to be kept in order and not to be desecrated,鈥� he told the WA Today website.
鈥淎s Muslims we are not meant to eat pigs, but that doesn鈥檛 mean we should not respect them for what they are,鈥� he added of the animals.
Samnakay said whoever left the carcasses at the cemetery should be forgiven as it was 鈥渕onth of forgiveness鈥� during Ramadan.