Police alleged he used a sign found in the street to smash the rear window, damaging a vehicle in Redlynch, an outer suburb of Cirns about 2.45am (AEST) on Monday.
Burgess is to front Cairns Magistrates Court on July 10.
He issued a statement through the club on Tuesday, apologising for his behaviour.
"I would like to apologise unreservedly to the Rabbitohs' members, sponsors and everyone in the community," Burgess said.
"I have let my team and my family down.
"I acknowledge that I am a role model for kids and I will do everything I can to restore my reputation through working harder in the community.
"It is my responsibility to ensure that this type of behaviour does not happen again.
"I will learn from my mistake and bounce back stronger and better as a person."
The Burgess incident was another black eye for rugby league, coming a day after NSW State of Origin winger Blake Ferguson was charged with indecent assault following an incident with a female patron at a bar in Cronulla on Sunday night.
- AAP