Thomas Vermaelen handed Wilshere the armband when he was forced off injured during the midweek victory over West Ham, and the midfielder is likely to lead the side out for their FA Cup tie at Brighton.
At 21 years and 25 days Wilshere is 55 days younger than Tony Adams was when he became skipper, and the England international has long been considered a natural heir to the likes of Adams and Cesc Fabregas.
Wenger said: "Honestly, Vermaelen made that choice (against West Ham) and I let him make it. It is always interesting to see when Vermaelen is out who he feels spontaneously should be the captain. I did not want to stop him.
"Wilshere is naturally a guy who is not scared of anything on the football pitch and that is usually the sign of a leader. He wants to win and shows you that.
"Of course he will be one of the leaders of this club - in fact he already is. A leader is somebody who does everything on the pitch to help his team to win. And he does that.
"If you are asking me if I will take the captaincy away from Vermaelen? No. But I think Jack will be captain of this club one day.
"It is important that the player gets to the stage where he develops first completely into an accomplished football player and then takes responsibility to take care of other people."
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