Van Persie, who was in scintillating form before being injured on international duty against Italy in November, is back in training which is good news for his club and his hopes of being fit for the World Cup in South Africa in June.
"He is expected to return but don't expect miracles when a guy has been out for such a long time," Wenger said on Thursday.
"But we are happy to have him back and he is physically ... in good shape. We have just to get him back to full team fitness - that will take two to three weeks maximum.
"I would say two weeks but after that when you start to play you are not at your best. You have to get a few games to get back to your best," the Frenchman added.
Arsenal, two points behind Premier League leaders Manchester United, are hopeful Nicklas Bendtner will be fit for Saturday's trip to Birmingham City.
"I expect him to be available," Wenger said of the Denmark striker who injured his ankle against West Ham United last week.
