The Netherlands forward damaged ankle ligaments in a friendly international against Italy last month and is expected to be out for at least five months following surgery.
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That means that van Persie will play little or no part in the rest of the Gunners' campaign, but Wenger has no fears about the longer-term prognosis.
He told The Times: "When you have such a big surgery, the opinion of the surgeon is important. Will he be the player he was before? We had a clear answer, 'yes'.
"At the moment, he can't do anything. He's just sitting at home and waiting to work again.
"It's virtually the rest of the season, but I haven't said that to Robin. Hopefully, we'll have a good surprise."
Source: DSG