Hernandez, 35, is set to miss the remainder of the 2023 season and will undergo surgery to begin the rehabilitation process on a date to be determined.
With Hernandez's contract set to expire at the end of the season, the former Mexico international might have played his last game for the Galaxy, and there will be fears that the injury could even be career-ending.
However, Galaxy head coach and sporting director Greg Vanney backed Hernandez to make a full recovery.
"I'm gutted for him, obviously this is never an injury anyone wants to have to deal with," Vanney said during a media availability session Friday. "It's a tough one, it's a long period of time and you got some work to do to get yourself back.
"I know with his work rate and with his passion and desire to be out there, he's going to do the work and he's going to put himself in position to come back and continue to play the game."
Hernandez suffered the injury in the 24th minute of Wednesday's 3-2 defeat to Real Salt Lake in the U.S. Open Cup. He was taken off the field on a stretcher after he went to the ground on a noncontact play.
"It's always a tough moment and the team has to process it too," Vanney added. "He's the captain, he's a guy that's a leader for the group and a vocal leader for the group so the group has to process the fact that he won't be with us again for this year and move on and keep attacking the next game."
Hernandez had scored one goal this season in 12 league and cup appearances. Overall, he has scored 39 goals in 80 league and cup appearances since signing with the Galaxy prior to the 2020 season.
The charismatic forward has long been one of Mexico's most popular players and is the country's all-time leading goal scorer, with 52 goals in 109 international appearances. He broke in with CD Guadalajara in 2006, and went on to star for Manchester United, Real Madrid, Bayer Leverkusen, West Ham United and Sevilla.
The news continues a season to forget for the Galaxy. After 15 games, the record five-time MLS Cup winner has the worst record in the league and sits at the bottom of the Western Conference with just three wins and 12 points.
Amid fan protests that began at the start of the season, the Galaxy announced at the end of May that they had fired club president Chris Klein. L.A. has failed to make the MLS playoffs in four of the past six seasons.