Inés and Maxima's father, Jorge Zorreguieta, died a year ago at the age of 89.
Zorreguieta appears to have committed suicide, the Dutch embassy in Argentina told Euronews in an email.
Zorreguieta's body was found in her flat in Buenos Aires, the Argentinian news agency Telam reported.
Tributes were paid to the "very attractive and talented" Zorreguieta on a video her brother Martin posted of her singing and playing the guitar past year.
Also shown in this family picture taken on the baptism of Princess Ariane in 2007 are (front row) Queen Maxima with Princess Ariane on her lap, King Willem-Alexander (centre right), and their daughters Princess of Orange Catharina-Amalia (left) and Princess Alexia (right). She is also godmother to the couple's youngest daughter, 11-year-old Princess Ariane. "It is intensely sad and heartbreaking news that can hardly be comprehended for those who stay behind", Prime Minister Mark Rutte said, according to The Guardian. In 2010, while she attended the University of Belgrano in Buenos Aires, Zorreguieta wrote a thesis centered on suicide in order to receive her psychology degree.
She is said to have worked as a civil servant in Buenos Aires.