According to the Guardian report, the arrest followed three men - including Robertson - being charged for trespass and being a public nuisance, at both the Kuraby mosque and the Darra mosque.
The immigration minister said the Kiwi had been counselled by immigration authorities about his history of extremist rhetoric when he first moved to Australia.
The New Zealand preacher made headlines last year when he delivered a sermon calling for gay people to be shot.
Footage posted online at the end of July showed Robertson, who was based at a west Auckland church, making highly offensive comments against homosexuals.
His words were roundly condemned by another Christian leader, Reverend Helen Jacobi of Auckland's St-Matthew-in-the-City, who said the video was verging on both hate speech, and criminal behaviour.
When contacted by the Herald at the time, Robertson said he did not deny his words were hate speech.
But he said he was just repeating the Bible - specifically Leviticus 20:13 which calls for gay men to be put to death.
Robertson moved to Australia with his family late last year, and opened a church in Brisbane.
Minister Dutton said a full investigation would be carried out by the Queensland police before a final decision about Robertson's deportation was made.
The incident also prompted a spokesman for the Islamic Council of Queensland to call for stronger laws around hate speech, to protect worshippers of all faiths.
"This is not just about Muslims, it's about hate," Ali Kadri told the Guardian.
"It's about dividing society, and if we don't nip it in the bud it will affect society as a whole."
