A hospital in Bangkok where passengers are being treated said there were spinal cord, head and muscle injuries.
There were 211 passengers – including many Britons, Australians and Singaporeans – and 18 crew on board the Boeing 777-300ER aircraft at the time of the incident.
The company said it would offer a full fare refund to all passengers on the flight, including those who did not suffer any injuries.
On top of this, Singapore Airlines said passengers will received delay compensation in accordance with European Union or United Kingdom regulations.
The airline also offered S$1,000 ($739; £580) to all passengers to cover immediate expenses and it arranged for loved ones to fly to the Thai capital where requested.
Under international regulations, airlines must offer compensation when passengers are injured or die while on a plane.
The incident brought attention to seatbelt practices, as airlines usually allow passengers to undo their belts during normal cruise conditions.
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