The aircraft's right engine caught fire after the aircraft, a Boeing 777-300ER, touched down at Changi airport at around 6:50 am (2250 GMT).
Emergency services put out the fire and there were no injuries to the 222 passengers and 19 crew on board.
Video provided by a passenger who identified herself as Bee Yee, showed the right wing on fire before being put out by fire fighters on the ground.
The SIA flight SQ368, departed at 2:05 am, but about two hours into the flight the pilot announced there was an engine problem and the flight would return to Singapore, Channel News Asia reported.
SIA's only accident resulting in casualties was a flight from Singapore to Los Angeles via Taipei, where it crashed on October 31, 2000 into construction equipment on the Taiwan Taoyuan International Airport after attempting to take off from the wrong runway. The crash killed 83 of the 179 people on board.
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