“It is clear that these arson attacks were designed to intimidate and influence those that attend this mosque and the wider Islamic community,” Assistant Commissioner Ian McCartney said on Sunday.
Australia, a staunch US ally that has sent troops to Afghanistan and Iraq, has been on heightened alert since 2014 for attacks by home-grown militants returning from fighting in the Middle East, or their supporters.
While there have been several “lone wolf” attacks, officials say 13 significant plots have been foiled in that time.
Police say the three men were adherents of militant Sunni Muslim ideology.
Police said the arrest of the man on Saturday came after extensive investigations into fires at the Melbourne mosque – but said it did not relate to any direct threat to the community.
The other two men facing charges are in custody and awaiting trial for allegedly planning militant attacks around Christmas Day 2016 in Melbourne.
The two, a 25-year-old and a 27-year-old, will also be charged with terrorist offenses for causing a previous fire at the Imam Ali Islamic Center in November 2016.
The man arrested on Saturday will appear in Melbourne Magistrates’ Court on Sunday, while the other two will appear in court on Monday.
This month, two men were charged with terror-related offenses after authorities disrupted what they described as a Daesh-inspired plot to bomb an Etihad Airways flight.
Another man arrested in relation to the foiled plot was charged with weapons offenses and released on bail. A fourth man was released without charge.
A gunman in a 2014 Sydney cafe siege boasted about links with Daesh militants, although no direct ties with the group were established. The gunman and two other people were killed in the siege.