While a date for his return has yet to be revealed, the 23-year-old is not expected to resume training for up to six weeks.
"The attacking midfielder sustained the injury during his national team's match against Chile," a club statement read. "He will now undergo a period of rehabilitation and is expected to return to training with the first team towards the end of October."
Lo Celso has made three Premier League appearances off the bench since joining Tottenham on deadline day on an initial season-long loan from Real Betis.
A prolonged absence for Lo Celso results in Tottenham losing yet another summer signing to injury less than a month into the new season.