The 24-year-old striker is set to return for rehabilitation in his native Holland as he recovers from a thigh problem - the latest fitness setback of what has been an injury-plagued season.
Wenger brought the forward back into the side for the first leg of the Carling Cup semi-final against Tottenham at the Emirates Stadium on January 9, but substituted him at the interval.
Following a bout of 'flu, medical tests have revealed a "little recurrence" of Van Persie's thigh injury, which will see him spend probably the best part of a month on the sidelines once again, and possibly become a doubt for the Champions League clash with AC Milan on February 20.
"We do not think it will be a long-term problem," said the Arsenal manager.
"Maybe we made a mistake to play him in the Carling Cup, because we wanted to rush him a little bit back after the muscular problems and were not cautious enough maybe on the night.
"This time we will have to be very patient."
Wenger added: "When a player has waited for so long and is ready to play, you are under pressure a bit from him as well because he feels he can play.
"Also, when you have been out for a few months, you need some games to get back to your best. You want to give him those games as soon as possible.