Coach Gerardo Martino has also lost Pablo Zabaleta and Lucas Biglia calling up San Lorenzo defender Emmanuel Mas and River Plate midfielder Matias Kranevitter in their place.
Martino, who announced his squad a week ago, may name more players for the tour with friendlies against Bolivia in Houston on Sept. 4 and Mexico in Dallas four days later, the AFA said on its website.
Argentina are using the tour to prepare for their opening South American 2018 World Cup qualifiers in October.
Di Maria has just joined Paris Saint-Germain from Manchester United and needs to work on his fitness while his PSG team mate Pastore is nursing a leg muscle injury.
Manchester City right back Zabaleta is out for at least a month with a damaged knee ligament while Biglia suffered an injury to his right leg playing for Lazio last weekend.
Local media speculated Martino would name Nicolas Gaitan of Benfica and Atletico Madrid's Angel Correa to replace Di Maria and Pastore.
Atletico reported that Argentina under-20 forward Correa had already been called up.
"Correa has been called up by Gerardo 'Tata' Martino for the ... next two friendlies, which means his first call-up to the senior (Argentine) national team," they said on their website (www.clubatleticodemadrid.com).
(Additional reporting by Luis Ampuero; writing by Rex Gowar, editing by Pritha Sarkar)
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