Passengers said the plane shook and bangs came from the right engine of AirAsia X flight D7 207 following its departure from Australia's Gold Coast to Kuala Lumpur late Monday.
The flight carrying 345 passengers and 14 crew was diverted to Brisbane airport just north of the eastern city and landed safely, the Malaysian carrier said.
"Two bird remains were found on the runway," the low-cost carrier said in a statement, adding that the starboard engine had experienced a "suspected bird strike".
"We are following all regulatory guidelines to ensure the safety and well-being of our guests, who are currently being attended to by our ground staff," AirAsia X chief Benyamin Ismail added.
"We would like to commend our pilot and crew members for their professionalism and swift action to reassure passengers who were on board flight D7 207 and to land the aircraft safely in Brisbane airport."
The Malaysian airline said it was arranging a special flight to take the passengers to Kuala Lumpur.
Passenger Calvin Boon said he saw flames going through the engine.
Another passenger, Tim Joga, told The Sydney Morning Herald the plane started to vibrate minutes after take-off.
"The plane started shuddering then there were a couple of loud bangs and a lot of light, "Joga said.
"I could see an orange light coming from the windows."
Another AirAsia flight from Perth to Kuala Lumpur experienced technical issues about 90 minutes into the journey on Sunday and was forced back to Australia, with one passenger saying the plane was "shaking like a washing machine".
The airline suffered its first fatal incident in December 2014, when AirAsia Flight QZ8501 crashed in stormy weather off Indonesia killing all 162 people on board.
That followed two Malaysia Airlines tragedies in the same year which left hundreds dead, raising concerns among some travellers about the safety of the country's carriers.
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