Queen Maxima, 46, the wife of King Willem-Alexander, was in Buenos Aires to be with her father as his condition worsened.
The funeral will be a private family event today. The royal couple and three daughters will be there, a family statement said.
Zorreguieta was a businessman, influential in the country's sugar industry and official in the government of Argentina's final military regime, from 1976-1983, under Jorge Videla.
He always maintained that because he was a civilian, he was unaware of Dirty War atrocities taking place while he was a cabinet minister.
The queen's mother chose not to attend without her husband.
Maxima has been queen consort since 2013, when Beatrix abdicated.
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