Zorreguieta's passing was confirmed by confirmed by Trudy Hulscher of the Royal House's communications department, E!
"The sudden death of Queen Máxima's sister comes as a big shock".
Tributes were paid to the "very lovely and talented" Zorreguieta on a video her brother Martin posted of her singing and playing the guitar previous year.
It's understood the 33-year-old took her life, a Dutch government spokesperson told local TV news.
Dutch state-run news agency RVD said the queen was "very shocked and very upset by the news". Her father Jorge Zorreguieta, Argentina's former agriculture minister, died previous year.
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Zorreguieta was a bridesmaid at her sister's wedding to then-Dutch Crown Prince Willem-Alexander in 2002 and was godmother to their youngest of three daughters, 11-year-old Princess Ariane.
Zorreguieta was a psychologist who once worked for an office on social policies at the president's office. She was suffering from depression, the BBC reported. Her expected schedule had included the opening of musical event the Holland Festival, and next week's royal tour of Latvia, Estonia and Lithuania.
The queen and her sister are native Argentinians.
If you or someone you know needs help, please call the National Suicide Prevention Lifeline at 1-800-273-TALK (8255).