The 27-year-old, who spent last season on loan at Real Madrid, injured himself in the 40th minute of Mexico’s warm-up match against Honduras ahead of the Concacaf Gold Cup, colliding with opposition defender Brayan Beckeles.
Any significant injury will come as a blow to Hernandez, who is playing for his future at Old Trafford.
United plan to make a decision on the poacher when he returns from international duty, after Real Madrid declined to make last term’s loan into a permanent signing.
Hernandez made just seven La Liga starts last season, and 16 substitute appearances, scoring seven league goals.
He was signed for United by Sir Alex Ferguson in 2010 and has 37 Premier League goals in 49 starts, six goals in 11 in the FA Cup, six in eight in the League Cup and 10 in 17 in the Champions League.
Hernandez has 40 goals in 74 appearances for Mexico.