Two of the men are already in custody and awaiting trial on suspicion of plotting bomb attacks in Australia's second largest city last year, while a third – a 29-year-old Melbourne man – was arrested late on Saturday.
All three face a maximum penalty of life imprisonment over the arson attack at the Imam Ali Islamic Centre in December 2016.
ISIS promotes the Sunni branch of Islam, and has branded Shi'a Muslims as heretics.