Wenger said that Van Persie has earned the respect of his teammates with some outstanding performances during this campaign.
"He took his role seriously on and off the pitch and I think it added something to his determination as well," the Frenchman told Arsenal Player.
"That is why maybe his commitment was even stronger - because he feels more responsibility. He grew into this role.
"The best way to be a captain for me is to be a fantastic football player, that is the best way to get respect in your team. He did that remarkably well."
Van Persie joined the Gunners from Dutch side Feyenoord in 2004.