One passenger reported hearing a "massive bang" before the aircraft turned back and Indonesian TV showed pictures of debris on the ground near Batam airport which it said belonged to the Qantas plane.
Authorities said none of the 459 people on board the Qantas flight was hurt in the most serious incident for the world's largest passenger plane in three years of commercial flight.
"This was a significant engine failure," Qantas Chief Executive Alan Joyce told reporters in Sydney. "We are not underestimating the significance of this issue."
Qantas A380s use Rolls-Royce Trent 900 engines. Rolls-Royce, whose shares were down more than 5 percent, said it was working with authorities to understand the incident.
Planemaker Airbus said it will provide full technical assistance to Australian and French accident investigators.
One of the Airbus A380's four Rolls-Royce engines failed minutes after it had left Singapore for Sydney. Qantas CEO Joyce said the plane was capable of flying on two engines.
Passengers said they saw parts of the engine fall off.
"I just heard this massive bang, like a shotgun going off," Tyler Wooster told Australia's Network Nine television. "Part of the skin had peeled off and you could see the foam underneath, pieces of broken wires sticking out."
The flight had begun in London.
Qantas, which operates six A380s, said it was grounding the aircraft pending a full investigation. Three A380 flights scheduled for Thursday, one originating in Sydney and two in Los Angeles, have been scrapped.
"We will suspend all A380 takeoffs until we are fully confident we have sufficient information about (flight) QF32," Joyce told reporters.
Singapore Airlines said it will delay all flights on its A380 fleet pending precautionary checks recommended by Airbus and Rolls-Royce.
It was not immediately clear how many flights would be affected or for how long.
The Australian Transport Safety Bureau was leading the investigation into the incident, Joyce said. Passengers will stay in Singapore overnight and another plane will be dispatched for them on Friday morning.
Initial media reports said the plane had crashed after an explosion over the Indonesian island of Batam, near Singapore.
There have been no fatal incidents involving A380s since they were launched in 2005 as the greenest, quietest — as well as the biggest — jetliner.
Shares in Airbus parent company EADS were down more than 4 percent by 1245 GMT. Qantas shares were little changed.
Emirates said it was not considering suspending flights as its engines are from a different supplier. European airlines Air France and Lufthansa said they would continue to use the aircraft as normal.
The plane involved in the incident was built in 2008.
More than 200 orders have been placed for the A380, and 37 are in operation worldwide, according to Airbus. The plane cost $17 billion to develop and has been dogged by production delays.
