On June 8, Flight SQ516 had experienced technical issues on the ground, resulting in a delay of two hours and 52 minutes.
In a Facebook post, Chandni Doulatramani, who was on the plane, claims that cabin crew were rude to passengers who had asked why the flight was delayed, the Straits Times reported.
In her post, accompanied by a video that has since been widely shared, Ms Doulatramani said that upset passengers, who had already boarded the plane, became more agitated when they were allegedly told to remain in their seats with their seat belts on.
The Singapore daily quoted her as saying, "When we confronted the cabin crew, they had no answers, rudely shut us up, threatened to call the cops to arrest us, and said 'We are in the same situation as you are, don't ask us, we don't know anything'."
In the video she posted, passengers are seen arguing with airline staff.
"We sincerely apologise for the inconvenience caused to our customers on board," the SIA said.
"With regard to the online post, we take these claims seriously and will be looking into them thoroughly," the airline was quoted as saying.