In a statement on Thursday, the club said Trengove, 18, had been drinking prior to the incident.
The penalty, half of which has been suspended, is the maximum amount a player can be fined under the AFL players' code of conduct.
The highly-rated teenager has footed the repair bill for the windscreen and apologised to the owners of the vehicle. He will also undertake extra club duties and receive additional counselling on responsible drinking.
The penalty was imposed by the Power leadership group and sanctioned by the club.
Port Adelaide football manager Peter Rohde said Trengove's actions were unacceptable.
"The club has reviewed all the circumstances and spoken to all parties involved in the incident. Jackson made a poor choice while under the influence of alcohol, and we do not condone his actions," Rohde said.
"Jackson is embarrassed and apologetic. It is disappointing for the Port Adelaide Football Club, as we take our social and community responsibilities extremely seriously."
Trengove was considered to be one of the steals of November's NAB AFL Draft when he slipped through to the Power's second-round pick at number 22.
The athletic tall has been eased into training at Alberton having overcome a serious knee injury. He joined his teammates for a near-full session for the first time on Monday.
