The Mail on Sunday says Van Persie sustained a serious ankle injury in Holland's friendly international match against Italy in Pescara.
Van Persie was rushed to hospital after just 12 minutes of the game when he collapsed to the ground following a heavy challenge from Italy defender Giorgio Chiellini.
Holland coach Bert van Marwijk said: "I was shocked when I saw it. It doesn't look good. I feel very sad for Robin and Arsenal."
Van Persie is expected to be examined in Amsterdam today by renowned ankle specialist Professor Niek van Dijk. The surgeon has previously treated Cristiano Ronaldo, Ruud van Nistelrooy and Michael Owen.
A team doctor said he feared Van Persie had ruptured ligaments in his ankle, an injury that would keep him out for at least three months. But if further examination reveals the ankle is broken, the star could miss the rest of the season.