Xhaka scored one of the goals of the season so far when finding the roof of the net from 30 yards against Hull City on Saturday afternoon, and he replicated that strike with Arsenal's opener in their 4-0 win over Nottingham Forest in the EFL Cup on Tuesday night.
The Swiss international only scored eight times in 132 appearances for previous club Borussia Monchengladbach after being deployed in a deeper midfield role, and Wenger admits that it was that statistic which led to him underestimating his new signing's shooting ability.
When asked if he was expecting goals of such quality from Xhaka, the Frenchman told Sky Sports News: "Honestly? Not really.
"When we looked at him, I knew he had a good shot but he played very deep last year and he didn't get forward a lot. I hope that will give him the taste for more."
Xhaka was making just his third start for Arsenal at the City Ground after making the £35m switch in the summer.