"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.
Asked if van Persie would be fit enough to line up against Argentina at Sao Paulo's Corinthians Arena, van Gaal replied: "I don't know.
"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."
Right-back Daryl Janmaat also trained apart from the main group at Sao Paulo's Estadio do Pacaembu and van Gaal revealed that he, too, was suffering from a stomach complaint.
However, there was better news for van Gaal concerning the fitness of Nigel de Jong and Ron Vlaar, both of whom trained alongside the rest of their team-mates.
De Jong had been effectively ruled out of the tournament with a groin injury, while Vlaar was considered a serious doubt to face Argentina due to a knee problem.
While van Gaal was delighted to see both players back on the training pitch, he said it was too early to say whether or not they would be able to face Lionel Messi and his Argentina team-mates.
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, the 29-year-old AC Milan midfielder, has not played since tearing a groin muscle during his side's 2-1 victory over Mexico in the last 16 on June 29.
Dutch medical staff initially predicted that he would be sidelined for between two and 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.
Should De Jong and Vlaar prove their fitness, it will be a major fillip for van Gaal, who has relatively few experienced players at his disposal.
The Netherlands are bidding to qualify for their second consecutive World Cup final, having been beaten 1-0 by Spain in the deciding match of the 2010 tournament in South Africa.