The car, going at 88mph, hit a pole causing a power cut and stopping the town clock, the spoof statement said.
The satire was among the first of what could end up being many tributes paid on Back to the Future Day.
Movie fans are celebrating 21 October 2015, the date Marty and Doc visited in the 1989 sci-fi time travel adventure sequel Back to the Future II.
The crash described in the police press release mirrors the key moment in the Back to the Future II plot, when Marty McFly, 17, and Doc go forward in time.
It said officers asked the 17-year-old driver what speed he had been doing, to which he replied, 88mph (142km/h) - the speed the pair's modified silver DeLorean had to hit to trigger the flux capacitor to send them back in time.
"A 17-year-old man was charged and was in possession of a licence which expired over 30 years ago," police said.
"Investigations into the vehicle and what a flux capacitor is, are ongoing."
It also posted an edited image of officers rushing to the scene on their hoverboards.
Mount Isa Cinema owner Jodi Saunders was quoted as saying the driver had asked when Jaws 19 - the film being screened at the Holomax cinema in the film - was showing.
Mount Isa Mayor Tony McGrady, meanwhile, was quoted as saying repairs were under way to save the clock tower, which in the famous scene is hit by lightning.
Queensland Police Media is famed for its light-hearted social media posts.
It has previously posted warnings on Facebook about wet roads from the tears of Top Gear fans after the show was cancelled, and has cautioned drivers not to "go ape" after a lorry carrying bananas crashed.
Police in Queensland say they have deployed their "hoverboard unit" after a silver car crashed near a cinema.