In a statement, Prime Minister Anthony Albanese said the incident in Ripponlea, in the city’s south-east, was “clearly aimed at creating fear in the community”.
“This violence and intimidation and destruction at a place of worship is an outrage,” he wrote.
“I have zero tolerance for antisemitism.”
He added that he had been briefed by the Australian Federal Police, who would provide support to authorities in the state of Victoria.
“The people involved must be caught and face the full force of the law.”
Victoria Police said the exact cause of the fire had not yet been determined and an arson chemist would visit the site.
However Det Insp Chris Murray said a witness had told them two people in masks appeared to have spread accelerant inside the building.
He appealed for anyone who may have witnessed the incident, or who may have CCTV or dashcam footage from the local area, to contact police.
Synagogue board member Benjamin Klein told The Age newspaper that people inside “heard banging on the door and the window, and some liquids came through which were lit”.
“The whole thing took off pretty quickly,” he said.
A man who was inside at the time, Yumi Friedman, added that a window had been smashed, sending “glass flying”.
Mr Friedman told reporters his hand was burned on a door knob when he tried to return to the synagogue to fight the blaze.
Det Insp Murray – who was confronted by an angry worshipper while updating the press – said police would be committing significant resources to the investigation and increasing patrols around the area.
“We’re going to do our best to make sure that they can return, as they should, to their local synagogues, doing what is absolutely Australian – that is to be able to worship without fear.”
Jewish community leaders have said they believe the attack is an escalation of a recent documented increase in antisemitism in Australia.
“None of the Jewish community is surprised. We’ve known this has been coming,” Executive Council of Australian Jewry president Daniel Aghion said.