"[Hernandez] will miss the remainder of the MLS is Back Tournament due to a right calf strain suffered in training last week," the club announced in a statement.
Galaxy coach Guillermo Barros Schelotto said in the postgame news conference that Hernandez is likely to be out for "three or four" weeks because of the injury.
The Galaxy have lost both their games in Group F and will need to defeat the Houston Dynamo on Thursday to have a chance of advancing to the round of 16.
Hernandez has had a mixed start to life in MLS, netting his first goal in the 2-1 loss to the Portland Timbers on Tuesday, but his club is still winless after four games in 2020.
The 32-year-old made the trip to the Disney-owned resort near Orlando, Florida, even though his wife is pregnant and they are in the process of moving into a new house.