The AC Milan midfielder was forced off the pitch with an injury less than 10 minutes into his side's 2-1 victory against Mexico.
"De Jong had a small groin strain and I was forced to substitute him," Van Gaal told reporters.
"I don't know if he will be available for the quarter-final, though to be honest it's very unlikely he will be able to play the next match.
"He is one of my most important players, so this is an enormous loss for us."
The Netherlands will face Costa Rica in the next round.