The British racer was arrested by the Australian police after they spotted him performing street manoeuvres known as a 'burnout' and a 'fishtail' with his silver Mercedes E500 in Melbourne.
Hamilton's car has been impounded under the anti-hoon laws and the police said that he will charged with improper use of motor vehicle.
"I was driving in an over-exuberant manner and as a result was stopped by the police.
"What I did was silly and I want to apologise for it," Hamilton said while rendering his apology.
Australia has outlawed tyre smoking stunts, called 'hooning', in a bid to prevent anti-social activities.
Hamilton's disgrace came just after he set the fastest time in practice for Sunday, Mar 28's Australian Grand Prix at the Albert Park racing circuit.