The Manchester United winger completed Sunday's 0-0 draw against Aston Villa in the Premier League but will not join up with the Argentina squad.
Argentina, who lead the standings on 18 points from eight games, visit sixth-placed Venezuela on Thursday and host Bolivia, who are eighth, next Tuesday.
Garnacho was initially called up for the two games, but coach Lionel Scaloni has now replaced him with Leicester City's Facundo Buonanotte.
Garnacho has seven caps and played in the Copa América in the US where Argentina clinched a record 16th title in July.
Argentina squad:
Goalkeepers: Geronimo Rulli, Juan Musso and Walter Benitez.
Defenders: Gonzalo Montiel, Nahuel Molina, Cristian Romero, Leonardo Balerdi, German Pezzella, Nicolas Otamendi, Lisandro Martinez, Marcos Acuna, Nicolas Tagliafico and Julio Soler.
Midfielders: Leandro Paredes, Alexis Mac Allister, Rodrigo De Paul, Exequiel Palacios, Enzo Fernandez, Giovani Lo Celso, Thiago Almada and Facundo Buonanotte.
Forwards: Nicolas Paz, Lionel Messi, Lautaro Martínez, Julian Alvarez and Valentin Carboni
