Detectives from Counter-Terrorism Investigation Group (CTIG) allege a 52-year-old man made “verbal threats” towards the centre in Caulfield on social media on Saturday.
The man was arrested in the Yarraman State Forest on Saturday night and had his phone seized.
He was charged with using a carriage service to menace, harass or cause offence and is due before Nanango Magistrates Court on January 16.
“As a result of a recent legislative change in Queensland, instances of serious vilification and hate crime are now a criminal matter,” police said in a statement.
“Where instances of hate or vilification are reported to police, investigations will be undertaken to prosecute those responsible.”