"Robin van Persie has an intestinal problem and I didn't want to take a risk," said van Gaal on the Manchester United striker, who trained apart from his team-mates on Tuesday morning.
"Tomorrow (Wednesday), I'll have to take all these decisions, not today. We have more than 24 hours before the match and Robin van Persie is a very important player for us.
"In principle, my captains always play, but only if they're 100 percent." However, the fitness condition of Nigel de Jong and Ron Vlaar is better now.
But van Gaal said it was too early to say whether or not they would be able to face Lionel Messi and Argentinian players.
Asked if De Jong would be fit to play, van Gaal told his pre-match press conference: "I have no idea. "He tried today in training. We'll now have to see how his body reacts. Let's wait for tomorrow, and for Vlaar as well."
De Jong has not played since after he got injured during his side's 2-1 victory over Mexico in the last 16 on June 29. Dutch medical staff initially predicted that he needs rest for two to four weeks.
Aston Villa defender Vlaar, 29, injured his knee during Holland's penalty shootout victory over Costa Rica in the quarter-finals.
Another player potentially available to face Argentina is midfielder Leroy Fer, who was able to take part in training despite a thigh complaint.