Van Marwijk said in Johannesburg that defender Joris Mathijsen was also in hospital for a scan on a knee injury.
"Robin van Persie is in hospital at this moment for a scan and Joris Mathijsen is the same. Robin has an arm problem and Joris a knee problem," he said at a press briefing after a training session.
He did not think the Van Persie injury was serious but wanted to see the scan first to be sure.
Netherlands knocked favourites Brazil out of the tournament on Friday with a comeback 2-1 win in Port Elizabeth in which Van Persie played 85 minutes.
Mathijsen had been named in the starting line-up against Brazil but was replaced after being injured in the pre-match warm-up.
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