The Imam Ali (AS) Islamic Center in Fawkner was gutted by the massive blaze on Sunday morning, which is being investigated by Victoria Police's arson and explosives squad and the Melbourne Fire Brigade, The Age reported.
Photographs reveal the word Daesh (ISIL or ISIS) in English and Arabic on the building, but it remains unclear what motivated the arson attack, which is believed to be the third incident in the past six months.
A member of the local Shia community who attends the Lawson Street prayer center said the fire would have a devastating impact.
"This is more than a place of worship. It is a place for education and information and community gatherings."
He refused to speculate on who might have been responsible.
"Everything is on the table and I don't think anyone really knows".
Mosques and Islamic community centers have been targets of repeated attacks by far-right groups across Australia.
Another community member said the graffiti was a ruse to distract investigators.
"I can tell you it has absolutely nothing to do with Islamic State [Daesh], and I hope the media and everyone else don't allow themselves to be manipulated. We have a very good idea who's behind this," the man said.