The Albiceleste are due to face Ecuador on Thursday before travelling to Bolivia next week, though Lionel Scaloni's side will have to make do without Lo Celso.
According to an injury update issued by the Argentine Football Association (AFA) on Tuesday, the 24-year-old suffered a left thigh issue during training at Tottenham and was unable to take part in a national team session on Monday.
Along with Udinese goalkeeper Juan Musso, Lo Celso - who has 21 senior international caps to his name - has now been sent back to his club for further assessment.
Tottenham will hope that the problem sustained by the former Real Betis midfielder is nothing serious as the club battle through a hectic fixture list.
Lo Celso has become a popular figure at Spurs since joining on an initial loan deal in August 2019, making 42 appearances across all competitions.
He has featured seven times so far this term, though was not selected for Sunday's 6-1 Premier League thrashing of Manchester United at Old Trafford after scoring twice in the 7-2 play-off win over Israeli side Maccabi Haifa three days earlier that sealed Tottemham's place in the Europa League group stages.
Lo Celso also missed the top-flight defeat by Everton on opening weekend because of a thigh injury.