Sanchez was substituted late in Chile's goalless draw with Colombia in an international friendly on Sunday (AEST).
The forward, who is on loan at Inter from Manchester United, will travel back to Milan for tests on an injury that may require surgery.
Sanchez has suffered a "dislocation of left ankle peroneal tendons", according to the ANFP, and will miss Tuesday's game against Guinea.
"Tests with magnetic resonance imaging and dynamic echotomography will be carried out to make the best therapeutic decision," said an ANFP statement.
Sanchez has scored one Serie A goal since leaving United for Inter, his sole strike coming in a win away to Sampdoria, during which he was sent off.
The 30-year-old may be a doubt for an upcoming Champions League double-header against Borussia Dortmund.
Inter hosts the Bundesliga side on 24 October then travels to Dortmund for the reverse fixture in Group F two weeks later.