Police have described those responsible for an anti-Islam graffiti attack on a southern Brisbane mosque as "brainless" criminals who left behind plenty of evidence.

A Rocklea home being used as a place of worship by Indonesian Muslims was targeted sometime between Tuesday night and Wednesday afternoon.

The words "die" and "Muslims are evil and have no respect for our ways" were spray-painted on the building.

It was the second Muslim prayer site in Queensland to be defaced in less than a week after a mosque at Mareeba in far north Queensland was vandalised last Friday.

Inspector Rob Graham said the offenders left plenty of evidence at the scene, which was also surrounded by security cameras.

"We are optimistic of determining who actually committed this brainless crime," he said.

"We are certainly not talking about criminal masterminds here. There was a number of pieces of evidence that were located in the near vicinity fingerprints and touch DNA are certainly going to shed some light.

"Also this is a place where there is a high volume of CCTV activity and we are very optimistic we will be able to determine who committed this offence in the near future."

Police said the vandals left 'plenty of evidence' at the scene. ( ABC News: Alyse Edwards )

Inspector Graham said they were still seeking assistance from anyone who may know who was responsible.

"We also seek assistance from anyone who might know who these people are or whether they were a member of a particular group who may have done this to come forward," he said.

"This is not the type of thing the police service or the wider Queensland community would condone."

Islamic Indonesian Community of Queensland president Hamid Mawardi praised police for their quick response to the spray-paint attack.

He said he had no idea who had vandalised the building but that it was "probably just kids".

"I think this is a misperception about Islam – we are here, Australian," he said.

Worshippers pray at the Rocklea mosque. ( ABC News: Alyse Edwards )

"I've been here for years and we live nice and peacefully and whoever did this – respect us as Australians."

Mr Mawardi believed youths could be behind the attack.

"I don't have any idea who did it. But I think this is probably a kid who doesn't know anything about what Islam is," he said.

"Probably just watching the TV and what's happening overseas and thinks Islam is all like this."

Muslim leader Ali Kadri said these types of attacks created a sense of fear in their community.

"Women especially will be very afraid to come and pray alone because women in particular have been targetted in the past so they'll be very afraid to come and pray here," he said.

On Wednesday afternoon, Queensland Police Commissioner Ian Stewart called for calm and tolerance in response to growing concerns over the threat posed by the terrorist group Islamic State (IS).

He was speaking after an incident in Melbourne on Tuesday night in which a man who was under investigation was shot dead by police, and after a number of counter-terrorism raids occurred in Sydney and south of Brisbane in recent weeks.