Hamilton, who came sixth in the Australian Grand Prix, had his Mercedes impounded by police and is expected to be charged for "improper" driving after spinning out the car's rear wheels at an intersection in sight of police on Friday.
Tim Pallas, the roads minister for the state of Victoria, was being interviewed by a radio station on Monday about a government-backed advertising campaign to educate young people about driver safety, in which the advertisements feature the slogan: "Don't be a dickhead."
Pallas was asked by the radio host about Hamilton's conduct. "He's certainly a very silly young man, quite frankly," Pallas said.
"Come on, you're the one who's using the language. Is he a dickhead?" the host pressed.
"Well, yes OK, I'll say it, he's a dickhead."
Pallas also said Red Bull's Mark Webber was "irresponsible" after the Australian driver was quoted by local media as saying the country had turned into a "nanny state".
"It's certainly changed since I left here -- it pisses me off coming back here, to be honest," Webber was quoted as saying following a question about Hamilton's driving offence.
"It's a great country but we've got to be responsible for our actions, and it's certainly a bloody nanny state when it comes to what we can do," he added.
Pallas said Webber's comments were not as serious an issue as Hamilton's brush with the law.
"I draw the line at Mark, because I think what Mark Webber has done has been totally irresponsible, but he didn't display the behaviour that Lewis Hamilton did, and that was put people's lives at risk," he added.