Van Persie was stretchered off during Holland's goalless friendly draw in Italy on Saturday night.
He damaged his ankle in a challenge with Giorgio Chiellini in the early stages of the clash.
Afterwards Dutch coach Bert van Marwijk suggested Van Persie had torn his ankle ligaments, although the extent of the injury will not be determined until Sunday when tests will be carried out on the striker.
If confirmed, Van Persie would be facing around two months on the sidelines - something which would threaten to derail Arsenal's Premier League title challenge.
Van Persie has scored seven league goals for the Gunners this season, helping them to second place in the current standings.
They trail leaders Chelsea by five points but have a game in hand on their London rivals.