Such therapy is no longer rare in the modern game, as players seek all they can to help get them back into action sooner rather than later.
Wenger can understand their reasoning, even if he does not agree with the logic.
"I am not a fan, but also I am not a doctor," the Arsenal manager said.
"I have seen a few bizarre treatments.
"I could tell you a few stories, I have enough to write a book on them.
"But I respect the individual freedom of everybody who wants to be treated how they want to be treated.
"Since I have been in the sport, when I have any guy who is injured, their first reflex is to go to their own country to be treated.
"When I was in France, the English players want to come back to England, here, the France players want to go back to France.
"That is a problem of confidence. Robin is exactly the same - most of the time he is treated first in Holland, because that is where he feels the most comfortable."
Wenger added: "The positive news we had is that originally I was told he could be out for the rest of the season, but it did not need surgery.
"Robin will be out for four to six weeks. We count six because we are a bit pessimistic."
The loss of van Persie was quickly followed by reports defender Kieran Gibbs had broken his foot while on duty with the England Under-21 team.
However that turned out to be no more than superficial damage and he could be back in action for the visit of Chelsea next weekend.
Arsenal have at least been boosted by the return of England forward Theo Walcott from a knee problem, while Brazilian midfielder Denilson is also in the squad for Saturday's trip to Sunderland.
The free-scoring Gunners had been on an unbeaten 13-match run through all competitions before the international break, which had lifted them up to second in the Premier League table.
Given striker Nicklas Bendtner is still sidelined by a groin problem which needed surgery, Wenger is set to turn to Croatia marksman Eduardo - who earlier in the week agreed a new contract with the Gunners - to lead the line at the Stadium of Light.
Wenger knows the importance of securing what would be a seventh win from eight in the Premier League.
"We have a game in hand. If we win that, we can be two points behind Chelsea, and we play them next week," he said.
"But in our job, the most important game is always the next one.
"The game against Chelsea has more significance if we win tomorrow."
Wenger added: "Sunderland are a team with a lot of dynamic, movement and commitment. That is always very difficult to handle.
"It is always a great atmosphere up there and I am highly conscious it will need a great performance from our side to win, but the players are focused."
Arsenal 8/13, Draw 13/5, Sunderland 5/1