Garnacho had been named in Lionel Scaloni's group for World Cup qualifiers against Venezuela and Bolivia, alongside club team-mate Lisandro Martinez.
However, the 20-year-old has been managing an issue over the last week and confirmed via Instagram that he would not be travelling to South America.
“I won't be able to be with the national team but I hope to recover so I can be on the next date,” the winger wrote.
Alejandro made his debut for La Albiceleste last year and has seven caps to his name.
Fellow Academy graduate Mainoo, meanwhile, was the only Red set to represent England, as Lee Carsley's side prepare for UEFA Nations League encounters with Greece and Finland.