The Mexico international picked up the strain in training on Thursday evening, sources told ESPN's Stefano Fusaro. A substantial recovery period could mean Hernandez's participation in the MLS is Back Tournament is in doubt, given the group stage comes to an end for the Galaxy on July 23 and the final is on Aug. 11.
Hernandez scored his first MLS goal in the Galaxy's 2-1 loss to Portland Timbers, but failed to convert a penalty and another clear scoring opportunity.
LAFC will be without star forward and reigning MLS MVP Carlos Vela, who decided not to attend the tournament due to his wife's pregnancy.
The loss of Hernandez leaves the Galaxy without two key players. Midfielder Jonathan dos Santos did not join the team for the tournament after undergoing hernia surgery.
Hernandez, who is the all-time leading scorer for Mexico's national team, has international experience with several top clubs including Mexico's Guadalajara, England's Manchester United, Spain's Real Madrid and Germany's Bayer Leverkusen.