The incident started about 3am over the Indian Ocean, around 700km northeast of Perth.
"As a precaution the aircraft descended to 10,000 feet and the captain requested a priority landing," Qantas said in a statement.
A Qantas spokesman said the jet, which landed safely, was being inspected.
"It was a fault with the air conditioning so the engineers are having a look at that now," he told AAP."It's taking a little bit of time to get to the bottom of it."
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The jumbo was expected to return to Sydney later on Monday. "It will fly back empty," the spokesman said.
Passenger Courtney Atkinson said on Twitter that the plane dropped 10,000 feet in four minutes.
Fellow passenger Nigel Richardson tweeted that an "emergency descent" was announced to cabin crew.
He said it was the "fastest descent I've ever experienced in a plane" and said cabin crew were running.
Mr Richardson tweeted pictures from the cabin showing all was calm on board.
"Full shut down of air conditioning system that keeps plane pressurised at altitude was the problem," he tweeted.
Mr Richardson praised the response of the crew to the emergency saying "#qantas first officer walking through plane giving personal situation update to everyone as best he can. Full marks to crew #QF2".
Another passenger told Australia's Nine News that the descent was "scary" but he did not find it "that dramatic".
"The cabin crew and the pilots under the circumstances did really well. They gave us as much information as they could, they explained exactly why they were doing everything," the passenger told Nine News.
"Diving from 40,000 feet to 10,000 probably sounds more exciting than it actually was. I think it was quite controlled and it was probably a little bit scary but because they gave all the information they could, I felt fairly reassured.
"I think under the circumstances they did quite well."
No one was injured in the incident.
Passengers have been given accommodation and will be booked on the next available flight to their destination.
- AAP, nzherald.co.nz
