The comment on the Instagram account of the recently-opened Australian Islamic House in Sydney included the apparent reference to the massacre of 51 worshippers at a New Zealand mosque in 2019.
It came almost six years ago to the day of the Christchurch shootings, perpetrated by an Australian man during the holy month of Ramadan.
West Australian police on Tuesday arrested a 16-year-old boy in Eaton, south of Perth, NSW investigators said.
The teen was helping police, a statement said.
Lebanese Muslim Association secretary Gamel Kheir said the tight-knit community had rallied together after the threat against the western Sydney mosque.
"Sadly it's not the first event nor an isolated event," he told ABC radio on Wednesday.
In a pointed message to political leaders, Mr Kheir warned the use of inflammatory language could embolden the public.
"Politicians need to stop playing political football with the idea of anti-Semitism and Islamophobia," he said.
"For politicians to come out blatantly ... only enables and emboldens these comments made allegedly by a 16-year-old child."
There has been an explosion in reported incidents of Islamophobia and anti-Semitism, amid simmering tensions over the conflict in Gaza.
However, community leaders have praised the swift police response and allowing prayers to continue with the assurance of their presence.
Australian Islamic House president Mazhar Hadid said places of worship needed to be safeguarded from hatred and violence.
"We are profoundly concerned by this threat and take it with the utmost seriousness," he said.
"We also urge the public to remain vigilant and to stand united against Islamophobia and all forms of bigotry."
Police said they did not believe there was an ongoing threat to the community.
Deputy Prime Minister Richard Marles joined other politicians and religious figures in condemning the "appalling reference" to the Christchurch attack.
"There can be no tolerance of this ... it is fundamentally anti-Australian to be engaging in this kind of activity," he told ABC TV.
"There is no place for Islamophobia in our nation and it's really important that we are standing with that community today and we are calling this out for what it is."
The mosque officially opened on Friday, the first day of Ramadan.
Australia's special envoy to combat Islamophobia, Aftab Malik, said the threat represented a chilling message to Muslims as they gathered to worship and break fast on a daily basis.
"This incident is the nightmare of every mosque and Muslim," he said.
"It is an escalation of the very real Islamophobia that Muslims across Australia experience and yet so many still refuse to believe exists."
Prime Minister Anthony Albanese and NSW Premier Chris Minns have vowed whoever was responsible for the threat would face the full force of the law.
