"Board staff have notified the leaders of the Muslim community of this incident."
The spokesman said the incident was the first of its kind.
"It is being treated as an isolated occurrence. If any members of the community witnessed any unusual goings on at the park we urge them to contact Crime Stoppers immediately."
Iqbal Samnakay, of WA's Muslim Social and Sports Association, said the apparent desecration would be upsetting to all sections of the community.
"Whether it is the Muslim community, or any other community, these burial sites should be respected," Mr Samnakay said.