The 23-year-old was the target of several heavy challenges during Argentina's bruising 0-0 friendly draw against Chile in Los Angeles last week and had to be withdrawn in the 53rd minute.
Charles Aranguiz caught the Spurs loanee with a crude studs-up challenge but Lo Celso later claimed the blow to his ankle was 'nothing to worry about'.
However, he will now miss his country's next game against Mexico, as well as Spurs' Premier League games against Crystal Palace, Leicester City, Southampton, Brighton & Hove Albion, Watford and Liverpool, their Champions League clashes with Olympiacos, Bayern Munich and Red Star Belgrade as well as their EFL Cup tie with Colchester United.
He is set to return to training at the end of October, so is unlikely to start in the club's first November fixtures - away games against Everton and Red Star Belgrade - either, meaning Spurs' home league game against Sheffield United may be earmarked by the new signing for a full debut.
Lo Celso, a summer signing from Real Betis, has made three substitute appearances for his new club so far this season, but has only amassed a total of 44 minutes in the 2-2 draws against Manchester City and Arsenal as well as the shock 1-0 defeat to Newcastle United.
Mauricio Pochettino appears to be easing him in slowly, despite the fact that the 22-year-old was a regular fixture for Betis last term, playing 45 times across all competitions for the La Liga outfit, scoring 16 goals and recording a further six assists.
The Argentine midfielder adds to his manager's injury woes, particularly in the centre of the park, with fellow new signing Tanguy Ndombele and Eric Dier also sidelined.
Additionally, Kyle Walker-Peters and Juan Foyth have struggled with their own fitness issues, meaning that central midfielder Moussa Sissoko and central defender Davinson Sanchez have been forced to deputise at right-back, further depleting Pochettino's central options.
Christian Eriksen and Jan Vertonghen were both recalled against Arsenal and Pochettino may have no choice but to continue to use the pair against Palace despite the speculation surrounding their futures.