The Swedish family travelled to Thailand on vacation.
Jenny Rosenberg, 36, and her husband Frederick, 35, were out snorkelling in the waters off Koh Mak, while their daughter, nine-year-old Ida were splashing around in the water close to the beach.
They immediately started swimming, as they heard their daughter scream in pain.
''We started swimming like mad towards the shore,'' Jenny Rosenberg told Aftonbladet.
Ida was knocked unconscious by the stings of the box jellyfish. A Swedish firefighter Anders Brunzell, 42, and his wife rushed to the girl's aid.
Aftonbladet and Scandasia quoted Mr Brunzell as saying: ''I and my family were sunbathing a bit away. We ran to Ida and saw that her right leg was completely covered with long threads, like glass noodles.''
They ripped off the tentacles with their bare hands and gave Ida heart massage and mouth-to-mouth ventilation.
Mr Brunzell asked the staff at the nearby hotel to get vinegar. Vinegar is the only treatment that will stop the spread of the box jellyfish's often fatal toxin.
Ida was moved by boat to the mainland, where an ambulance took her to a hospital in Trat province.
She is reported to be conscious, although badly burnt on the leg and other body parts by the stings. She is kept in hospital for further observation.
Mrs Rosenberg said: ''Because she was unconscious for so long, the hospital staff is worried that she has had brain damage. She is a bit groggy and still has a fever. But, everything else seems okay.''
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New York Times