Van Persie sustained a painful-looking injury during Saturday night's 2-1 friendly match loss against Benfica, and received lengthy treatment following the knock. He did not enter the fray for the second half.
Wenger has revealed left-back Gibbs and centre-back Vermaelen have also picked up issues ahead of the club's Premier League opener against Newcastle next weekend. The Gunners then face Udinese in the Champions League before tackling Liverpool.
First asked about Van Persie, Wenger said: "It is an ankle problem, I don't know how bad it is. Gibbs has a muscular [thigh] problem and Vermaelen has a slight back problem."
Wenger said: "They can include him as much as they want, he will not play [because of injury]."