Van Persie was carried off on a stretcher in a friendly between Netherlands and Italy earlier this month after landing badly following a tackle by Giorgio Chiellini.
"In order to repair his (right) ankle Robin will undergo surgery next week in Amsterdam to reconstruct the ligaments," Arsenal said in a statement on Saturday.
"The club's medical team anticipate a full recovery will take between four and five months."
Arsenal manager Arsene Wenger was furious with the Dutch FA (KNVB) and told Sunday's British newspapers:
"Countries just take your player away for a friendly and then give him back and say: 'There you go'.
"It doesn't happen in any other sport. It's a joke and is so disrespectful."
"Advice was sought from the leading ankle specialist Mr Niek van Dijk, who confirmed more extensive damage had been suffered than was first diagnosed," they added.
Wenger was also critical of the Dutch FA over their initial treatment of Van Persie's injury.
"We have just found out that it is much worse than what they told us," he said.
"If a player gets injured with his country he should be sent back to his club straight away to be checked out by their doctors, not by those of the national team."
Van Persie was quoted by British media as saying: "If I had known then, I would have been operated on the next day. We have all been steered in the wrong direction."
"It is so frustrating to be out for months," added Van Persie. "I was having a super season with the team. I had never felt as strong and powerful."
