Officers say the Toyota Hilux utility knocked down the gates to the property, in Brisbane's Margaret Street, shortly after 7pm on Friday.
The driver fled the scene before being taken into custody a short time later.
No one was injured during the incident.
Police said a 32-year-old Sunnybank man was expected to face Brisbane Magistrates Court on Saturday charged with wilful damage, serious vilification or hate crime.
He is also accused of dangerously operating a vehicle and possessing dangerous drugs and the utensils for their use.
Queensland Premier David Crisafulli has described the alleged attack as concerning and says Jewish Australians would be feeling deeply distressed by the incident.
"I have spoken to Jewish leaders, as well as police, and I want to assure Queenslanders we are taking this seriously," he wrote on social media.
"This is another signal as to why we have put strong laws before parliament to protect all people where they worship."
"We are going through the process and I fully intend to have them passed during the next sitting of parliament."
An inquiry into the proposed legislation has been told multiple stakeholders were not consulted before the bill was drafted.
The Federation of Islamic Councils, the Islamic Council of Queensland and the Ethnic Communities Council of Queensland all told the state's parliamentary committee for justice, integrity and community safety that they had been bypassed.
Under the laws, Queensland's attorney-general would have the power to outlaw phrases, the public uttering of which would be punishable by two years in prison.
Police say their investigation into Friday evening's apparent attack are ongoing.
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