The Arsenal forward will receive treatment in Santiago with the Chile squad, but may miss some crucial games for Arsenal.
"The medical team of the Chilean national team can confirm Alexis Sánchez has a low grade muscle tear. The player will stay in Santiago, under treatment and evaluation, ahead of Chile’s match against Uruguay," a statement from the Chilean football association read.
Sanchez could now miss Arsenal's trip to Old Trafford on 19 November should he not recover in time.
The Chilean has scored eight times for the Gunners this season, who sit in fourth place in the Premier League, two points behind leaders Liverpool.