The Mexico international was forced off in Bournemouth's opening friendly against German side St Pauli and will miss the start of the new season.
"He will be supported by the club’s medical department as he navigates a period of rehabilitation," Bournemouth said in a statement.
The 24-year-old has endured a frustrating run with injuries after suffering a quadriceps problem on loan at Celtic in March. He was also left out of Mexico's squad for this year's World Cup.
Bournemouth open their Premier League campaign at Manchester City on August 23.