The 18-year-old has been afforded increased first-team chances following injuries to the likes of Theo Walcott and Jack Wilshere, with Arsene Wenger hailing his "great" potential.
The 18-year-old, who joined from Stuttgart in 2010, has enjoyed a breakthrough season at the Emirates Stadium this year with five outings.
"He has technical ability, he has power, he has pace, he has finishing quality and he can give a final ball. He's a powerful offensive player and I believe that he will be a great player for Arsenal."
Gnabry has represented Germany at Under-16 to Under-19 level.