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."
Arsenal said on Saturday the injury had been expected to keep him out for between four and six weeks.
"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.
ANGRY WENGER
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."
The 26-year-old has thrived this season, scoring eight goals in his last 11 matches for third-placed Arsenal, who entertain Premier League leaders Chelsea on Sunday.
"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."
His ankle operation means the Dutch striker faces a race against time to be fully fit for the World Cup in June.
