The driver, whose name and other details were withheld by the police, is the second to be charged with sexually assaulting a passenger in the city in a week.
Queensland state police said the 37-year-old man raped the teenager in his car on July 8, and the girl reported the assault to police the next morning.
The arrest comes one week after another Uber driver was charged with raping a passenger three times.
Police said the two cases are not related.
The company in a statement said it had immediately blocked the 37-year-old driver’s access to the service after learning of the allegations against him.
“The behavior described by Queensland Police is absolutely deplorable and our thoughts are with the woman and her family,” the company said.
Despite the reported assaults, Police Acting Detective Superintendent Mick O’Dowd said officials are not concerned about Uber’s safety record.
“I don’t think from the actions of two persons you could draw a conclusion it makes Uber any less safe,” he told reporters.
“There are thousands of transports every day where people are collected and dropped at their destination without any problem at all.”