'Go back to your country' Qld man charged

A Queensland man has been charged after allegedly telling a Muslim woman to go back to her country.

Police allege the 66-year-old verbally assaulted the woman, who was wearing a niqab covering her head and face as she shopped at a supermarket at Logan, south of Brisbane.

"You are a Muslim, go back to your country," police claim the man told her.

He was arrested early on Friday but it's unclear when the encounter took place. The man is facing three counts of common assault, which covers verbal assault, and one count of obstructing police.

He has been admitted to hospital with an undisclosed condition and is yet to appear in the Brisbane Magistrates Court.

The arrest comes after a Brisbane man was charged with spraying menacing graffiti on a mosque at Rocklea, in Brisbane's south.

The 34-year-old man allegedly sprayed graffiti on the Rocklea mosque and has been charged with wilful damage, trespass, public nuisance and possessing a graffiti instrument.

He is due to face the Brisbane Magistrates Court on October 22.

In another incident, the word "Evil" was scrawled across a mosque at Mareeba, in far north Queensland, last week.

The incidents have come amid a heightened terror threat level in Australia and amid counter-terrorism raids in Sydney and Brisbane.

Police are also investigating an apparent anti-Islamic incident on the Gold Coast after a man was told he'd be "bashed" and "run over" by a group of four men in a car.

It's alleged the bearded man, who isn't Muslim, was stopped in traffic at approximately 6.30pm (AEST) on Thursday when the men in a white Commodore yelled the abuse at him.

"We won't tolerate someone being targeted because of their religion or race," Superintendent Mat Rosevear told AAP.

"Whether verbal or otherwise, they've actually committed assault, which is a crime. It's not something minor in nature."