The Chilean, on loan from Manchester United this season, suffered dislocated ankle tendons during a friendly match against Colombia on Saturday. National team boss Reinaldo Rueda says the veteran attacker could be out for "two or three months," according to the BBC.
Sanchez, 30, is slated to undergo an MRI in Italy to determine the severity of the ailment and whether surgery is required.
The former Arsenal star was off to an encouraging start with the Nerazzurri, scoring on his full league debut before impressing against Barcelona in the Champions League.
In addition to potentially losing Sanchez, the international break also stung Inter's backline, as full-back Danilo D'Ambrosio broke a toe on his right foot while featuring for Italy in Euro 2020 qualifying.