"The flight crew disconnected the autopilot and manoeuvred the aircraft in response," the Australian Transportation Safety Bureau (ATSB) told the newspaper in a statement.
"Fifteen passengers received minor injuries. As part of the investigation, the ATSB will interview the flight crew and gather additional information."
One of the 15 people to be injured required hospitalisation but was later released, it was reported.
The airline confirmed the incident to The Australian on Wednesday - the first public statement almost a week later.
"Customers on QF29 experienced unexpected in-flight turbulence when travelling from Melbourne to Hong Kong on Sunday," a Qantas spokeswoman said.
"We notified the ATSB of the occurrence, and our own teams are also reviewing the event."
Geoffrey Thomas, an aviation expert, told The Australian that such an incident was "extremely unusual".
"A stick shaker is an extremely rare event, and very, very serious," he said.