Sanchez, 27, will miss Chile's World Cup qualifier in Colombia on Thursday.
But the Chilean team's medical staff say the former Barcelona player could return for the home game against Uruguay next Tuesday.
"He will remain in Santiago, under treatment and in evaluation for the meeting against Uruguay," said a statement.
Sanchez, who has scored eight goals for the Gunners this season, played the whole 90 minutes of Sunday's 1-1 home draw against Tottenham.
Fourth-placed Arsenal go to Manchester United on 19 November in their next fixture after the international break.
Arsenal forward Alexis Sanchez has picked up a "low grade muscle injury" on international duty with Chile.