The 26-year-old Dutchman suffered the injury while on international duty in November and was initially expected to return to full fitness in six weeks.
But instead surgery was required, and Wenger concedes the problem
However, Wenger is confident Van Persie will bounce back from the injury and rediscover his top form next season.
He added: "When you have such a big surgery there is one thing that is important first of all, and that is the option of the surgeon, will he be the player he was before? We had a clear answer. 'Yes'.
"The second thing that is very important in the first stage after surgery is has he an infection or not? He hasn't.
"The third thing is patience. At the moment he cannot do anything, he is just sitting at home waiting until he can work again. The first two steps have been very successful."
Van Persie had been a key performer for the Gunners, scoring seven goals in 11 Barclays Premier League matches before being hurt.
will keep Van Persie sidelined for several more months.
Wenger told the official club website: "If you are very positive you would say [he'll be back in] April.
"If you're a bit cautious you say May. It is virtually the rest of the season.
"Personally I thought 'Let's put it in my head that he will not play again this season and hope that I will have a good surprise'."