Imams, Muslim community groups and politicians have condemned "vile" graffiti that was sprayed onto the Holland Park Mosque in Brisbane on Tuesday.

The graffiti included several Nazi swastika symbols, the words "remove kebab" and a reference to the Christchurch mosque shooter.

Queensland Police said they are investigating the act of "wilful damage".

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A coalition of Muslim organisations said the mosque, which dates back to 1908, is "an iconic landmark which is embraced by the broader local community".

In a statement, the Australian National Imams Council, the Islamic Council of Queensland and the Australia Muslim Advocacy Network, said Tuesday's act was "reprehensible".

"The Australian Muslim community is reeling from this incident. It is up to us as a nation to show that these acts do not define us," the statement said.

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"Such conduct is reprehensible and ought to be condemned in the strongest terms. At its core are sentiments of hate, violence and harassment."

Labor MP Stirling Hinchliffe condemned the incident, saying the Queensland community would react by coming together in unity.

"Queensland is a diverse state and these types of vile actions in no way reflect who Queenslanders are," he said in a statement posted on Facebook.

Labor MP Terri Butler offered her support, describing the graffiti as "disgusting vandalism".

"Our community is vastly stronger than the anonymous coward who did this," she said.

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Labor MP Joe Kelly said the "abhorrent vandalism ... is a disgrace".

"This is not how we operate in this community. We are a community that tolerates people, a community that celebrates diversity. We are a community of respect."

Labor MP Graham Perrett said the act has only hardened the resolve of the community to fight "against religious discrimination".