The 18-year-old, who joined from Stuttgart in 2010, has enjoyed a breakthrough season at the Emirates Stadium this term with five outings.
Gnarby has been afforded two Premier League starts following injuries to the likes of Theo Walcott, and scored is first proffesonal goal against Swansea City in September and Wenger has backed him to continue improving.
"We signed Serge Gnabry because I believe that he will be a great player," Wenger told the club's official website. "He's nearly there now, and competes for a regular place in the team in the Premier League
.
