Gnabry, 18, scored his first goal for Arsenal on Saturday's 2-1 victory at Swansea, where his pace and trickery caused problems for the hosts all evening.
Wenger has become known for developing young players in his 17 years at the club, with Cesc Fabregas perhaps his biggest success.
Gnabry's goal made him Arsenal's second-youngest Premier League goalscorer - Fabregas being the youngest.
And Wenger has been very impressed by the way the teenager, who was just 14 months old when he took charge of Arsenal, has contributed.
"He is surprising," said Wenger. "He has the talent, but he has the personality on the pitch as well.
"He doesn't look timid, he looks to play with belief and, of course, talent. Unfortunately he is another player for Germany, he's not English.
"He was one-year-old when I came to Arsenal, I can't believe it. Now I have some players in my squad who were not born when I arrived at Arsenal.
"The two players who scored (Gnabry and Aaron Ramsey) have a combined age of 40."
I don't think Arsene is truly surprised. He is trying to manage expectations from Serge. I saw him during pre-season and it was clear he would be in the senior squad. I hope he keeps improving,- ihatebullcrap