Sanchez lasted just 17 minutes of Chile’s 2-1 defeat to Argentina in the Copa America third-place playoff, before being replaced by Junior Fernandes.
The severity of the 30-year-old’s injury is yet to be confirmed, though it may force Sanchez to miss the entirety of United’s pre-season schedule.
Ole Gunnar Solskjaer and the United squad fly to Perth on Sunday ahead of friendlies in Australia, Singapore and China.
Sanchez may have been available for games against Kristiansund and Milan in towards the end of United’s pre-season, though a hamstring injury is likely to delay his return.
The Chilean faces an uncertain future at Old Trafford, having endured a difficult 18 months since joining from Arsenal last year.
United’s highest-earning player scored just two goals at club level last season and made only six starts following Solskjaer’s appointment as manager.
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