De la Fuente, who missed the away defeat and home win against South Africa this month, was included on Monday in the squad that will travel on Friday but has now dropped out.
He is replaced in the 28-man squad by Gabriel Azcarate, who could make his tournament debut if called into action during the away Tests, the Argentine Rugby Union (UAR) said.
Coach Daniel Hourcade said that De la Fuente had failed a medical before praising the Pumas' form.
I see the team in good form, more solid... We're going to prepare a strategy to try to beat (New Zealand) as we have always done," Hourcade said.
"The objective on this tour and in all our matches is to improve our game. We want to correct the things we didn't do well because this tour is the hardest part of this tournament for us.
"We're going to play against the best team in the world, who have just played a great series against Australia, but that doesn't intimidate us, on the contrary it motivates us."
Argentina face the world champion All Blacks, who top the standings after home and away wins over Australia, in Hamilton on September 10 and the Wallabies in Perth a week later.
Squad: Forwards: Nahuel Tetaz Chaparro, Felipe Arregui, Agustin Creevy (captain), Lucas Noguera Paz, Julian Montoya, Ramiro Herrera, Enrique Pieretto, Matias Alemanno, Guido Petti, Marcos Kremer, Juan Manuel Leguizamon, Pablo Matera, Javier Ortega Desio, Leonardo Senatore, Facundo Isa. Backs: Martin Landajo, Tomas Cubelli, Felipe Ezcurra, Santiago Gonzalez Iglesias, Nicolas Sanchez, Santiago Cordero, Ramiro Moyano, Gabriel Azcarate, Juan Martin Hernandez, Matias Moroni, Matias Orlando, Lucas Gonzalez Amorosino, Joaquin Tuculet.