Her body was removed from her apartment this morning and a post-mortem examination is expected to take place in due course.
Queen Máxima has cancelled a string of public engagements following news of the death of her youngest sister, at the age of 33.
The queen and her sister are native Argentinians.
Queen Maxima of the Netherlands, seen here with her husband, King Willem-Alexander, in 2017, was close to her sister, who was godmother to her third child, Princess Ariane. A spokesman for the Netherlands Government Information Service told Dutch media that Zorreguieta was believed to have died in a suicide.
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She was also godmother to Queen Maxima's 11-year-old daughter Princess Ariane and the youngest daughter of Jorge Zorreguieta and María del Carmen Cerruti.
"With our hearts and our thoughts we are with the queen and her family".
Ms Zorreguieta worked for the Argentine government as an official in the Ministry of Social Development. Zorreguieta reportedly suffered from depression and was seeking psychological help.
'I wish them all the strength they need to cope with this frightful loss.
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Queen Maxima, 47, also has two brothers, Martin and Juan, and three half siblings. She had also worked for the social development ministry in Buenos Aires province and at a United Nations office in Panama.
Inés Zorreguieta, the younger sister of Queen Maxima of the Netherlands, was found dead at her home in Buenos Aires, Argentina, on Wednesday night.
Jorge Zorreguieta worked as agriculture minister during Argentina's brutal military dictatorship.
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