The Queen, originally from Argentina, was said by the royal household to be "very shocked and very sad".
The 33-year-old Ines Zorreguieta was found dead in her Buenos Aires apartment on Wednesday.
Other details about her death were not immediately available, but Zorreguieta had reportedly suffered from eating disorders and depression.
Inés Zorreguieta (left) is Queen Maxima of Holland's (right) younger sister. A Dutch government spokesperson told Dutch NOS TV that her death appeared to be suicide.
Argentina-born Queen Maxima has cancelled all engagements on her upcoming agenda, the Royal Palace has confirmed.
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.
Zorreguieta was a psychologist who worked on social policies at the office of Argentina's president, Mauricio Macri.
Her father, Jorge Horacio Zorreguieta, died past year in Buenos Aires aged 89. I wish them all the strength necessary to carry this frightful loss together.
It's understood King Willem-Alexander will carry out next week's state visit next week to Estonia, Latvia and Lithuania alone, according to the BBC.
Between 2009 and 2011 she worked at the United Nations headquarters of Panama but returned to Argentina in 2012 after a breakup.