The trio, aged in their 20s, are each accused of engaging in a terrorist act over an arson attack that destroyed the Imam Ali Islamic Centre at Fawkner in December, Victoria and federal police say.
Two of those men, 25-year-old Ahmed Mohamed and 27-year-old Abdullah Chaarani, are already in custody over an alleged plan, separate to the arson attack, to bomb Melbourne landmarks on Christmas Day.
The third man allegedly involved in the destruction of the mosque is 29-year-old Hatim Moukhaiber, who was arrested after police pulled over his car at Roxburgh Park on Saturday night.
Mohamed and Chaarani are also set to be charged with an additional count each of engaging in a terrorist act over an earlier fire at the Imam Ali Islamic Centre in November.
"We're not saying that these are just arson attacks," Australian Federal Police Assistant Commissioner Counter Terrorism Ian McCartney told journalists in Melbourne on Sunday.
"What we're going to allege is these were IS-inspired attacks. They were inspired and designed to influence, put fear into a particular community."
Police said they did not have information indicating that IS directed the men to commit the alleged arson attacks.
"If you look at the type of attack and what the influence is ... this centre is a Shia centre," Victoria Police Counter Terrorism Command Assistant Commissioner Ross Guenther said.
"So what will be alleged is that those who committed this attack adhere to an extremist Sunni ideology."
"That leads us to the conclusion ... that that is part of an ISIS influenced or inspired attack."
Following the mosque attack in December, police said graffiti reading 'The Islamic State' in English and 'The State the Islam' in Arabic was sprayed on the outside wall of the centre.
Moukhaiber appeared in Melbourne Magistrates Court on Sunday while Mohamed and Chaarani are set to appear on Monday.
The duo are also due in the same court that day as part of a larger group accused of planning to bomb Flinders Street Station, Federation Square and St Paul's Cathedral on Christmas Day using an improvised explosive device and other weapons.
Mohamed, Chaarani, 23-year-old Ibrahim Abbas and his brother Hamza Abbas, 22, are set to face a five-day committal hearing from Monday.
