The 18-year-old German scored his first senior Gunners goal in Saturday's 2-1 Barclays Premier League win at Swansea, and his pace and trickery proved a constant thorn in the side of the home defence.
During his 17-year stint in charge of Arsenal, Wenger has been renowned for his ability to develop young players into first-team regulars.
Gnabry's goal made him Arsenal's second-youngest Premier League goalscorer - Cesc Fabregas being the youngest.
Gnabry may have a long way to go before he can be compared to players of Fabregas' calibre, but 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 the Frenchman. "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."