Zorreguieta was a psychologist who worked for an office on social policies at the president's office.
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.
Her father, Jorge Horacio Zorreguieta, died past year in Buenos Aires at age 89.
Zorreguieta enjoyed a close relationship with her sister, Máxima, and was bridesmaid at her wedding to the then Dutch Crown Prince Willem-Alexander in 2002.
"With our hearts and our thoughts we are with the queen and her family".
According to reports, Inés Zorreguieta worked for the civil service in Buenos Aires, and had been suffering from depression. She canceled her upcoming engagements including a state visit to Estonia, Latvia and Lithuania.