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.