The incident is said to have happened during a night out in Perth, and the Western Australia Assistant Commissioner Nick Anticich - who said the British boy band's superstar status didn't matter - has revealed an investigation is underway.
He told Perth Now: "I have been made aware of it, and I've asked our traffic enforcement group to have a look at it. We need to determine the facts and obviously if there's any evidence supporting the allegations.
"It's unacceptable behaviour. It breaches the law and we will deal with every person in the same way.
"By virtue of the fact that they are rock stars is not a license to break any laws or be any different from anyone else. One Direction they may be, but the only direction in relation to this type offending will be to the courts."
The group - made up of Louis Tomlinson, Harry Styles, Niall Horan, Liam Payne and Zayn Malik - were reportedly driven away in three Mercedes when they landed in a private jet, before attempting to bypass a group of fans.
Police Minister Liza Harvey insisted the investigation makes a point that nobody is above the law, but still gave the 'Best Song Ever' hitmakers a "warm welcome".
She said: "It's a clear message for everyone who uses our roads. We have really strong legislation in this state and that applies to everybody who visits here.
"We extend a warm welcome [to One Direction] but when you're here we expect you to apply the same standards that we apply to our community."