Emergency services and medical staff at the Learmonth air base, which lies about 1,100km northeast of Perth attended to the injured after the aircraft landed safely, Sergeant Greg Lambert of the West Australian police said.
"It is understood up to 40 people were injured during a mid-air incident," he said.
Reports suggested that about 30 passengers and crew had been hurt in the incident, with 15 of them sustaining injuries such as broken bones and lacerations.
"While cruising in level flight, the aircraft experienced a sudden in-flight upset, resulting in injuries to a number of cabin crew and passengers, primarily in the rear of the aircraft," the Australian Transport Safety Bureau (ATSB) said in a statement.
"The crew declared a mayday and diverted the aircraft to Learmonth ... where it landed without further incident," it said.
The ATSB has launched an investigation into the mid-air incident, it said.
Although Qantas has a generally safe flying record and has never lost an aircraft, there have been a string of safety-related incidents on its aircraft in recent months.
In July, 365 people escaped serious injury when an oxygen canister exploded and punched a hole in the fuselage of a Boeing 747-400.
Australian investigators in August announced a safety review of Qantas after two other incidents involving its aircraft occurred within two weeks of each other.
On July 28, a Qantas Boeing 737-800 returned to Adelaide after a landing gear door failed to retract, while in early August a Boeing 767 bound for Manila turned back to Sydney after developing a hydraulic fluid leak.
The Civil Aviation Safety Authority (Casa) later said there was no evidence to suggest any links between the three mid-air emergencies on Qantas flights.