The Singapore-bound Boeing 777-300ER was diverted to Bangkok and landed at 15:45 local (08:45 GMT).
Flight SQ 321 was carrying a total of 211 passengers and 18 crew, the airline said in a statement.
"Singapore Airlines offers its deepest condolences to the family of the deceased," it said.
The airline added that it was working with Thai authorities to provide medical assistance to passengers, and was sending a team to Bangkok to provide any additional help needed.
Thai authorities have despatched ambulances and emergency teams to Suvarnabhumi Airport.
Singapore's Transport Minister Chee Hong Tat said the government would provide assistance to the passengers and their families.
"I am deeply saddened to learn about the incident onboard Singapore Airlines flight SQ321 from London Heathrow to Singapore," he posted in a statement on Facebook.
AzVision.az
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