Police said the 23-year-old Brown Plains man was stopped on Buckley Road at Stockleigh about 2.20pm on Saturday for a side drug test, which tested positive.

The driver was issued with a 24-hour driver's licence suspension notice and a notice to appear for drug-driving.

It will be further alleged once the man was released from police custody, he returned to his car on Buckley Road and drove to the Baitul Masroor Mosque on Neville Road.

Police said the man allegedly drove into the closed front gates and caused minor damage while shouting offensive words through the open driver's window towards the people inside.

He then drove home where police arrested the man and further charged with wilful damage, committing public nuisance and driving a motor vehicle while suspended.

Speaking ahead of a prayer service in Karawatha on Sunday, police commissioner Ian Stewart said the alleged incident was not "born out of hatred".

"We can never legislate against stupidity," he said.

"Please do not be afraid because this was not anything that could be claimed as a hate crime.

"It was simply someone acting stupidly [allegedly] under the influence of drugs."

The mosque had dealt with incidents in the past, including a severed pig's head being left outside in 2017 that Ahmadiyya Muslim Community Queensland's Zain Baig described as a "disturbing sight".