The teenager suffered ankle-ligament damage in the 0-0 draw with Southampton and faces a spell on the sidelines, although Reds manager Erik ten Hag stressed he expects him to return before the season is out.
Some outstanding form this term prompted a senior call-up for the Madrid-born prospect, who qualifies for the South American nation through his mother.
However, he was forced to pull out as the world champions prepare for games against Panama and Curacao.
"It's a pity," said former West Ham defender Scaloni at a press conference.
"Garnacho was called up but he could not come due to an injury.