Julian Draxler, also a hamstring problem, and Mario Gomez (groin) will also miss the friendly at the Westfalenstadion.
Ozil has made 22 Premier League appearances for Arsenal this season and a further nine in cup competitions, but has not been part of Arsene Wenger's latest two squads because of injury.
The meeting in Dortmund presents England boss Gareth Southgate with his first game in charge as permanent manger of the Three Lions.
England then take on Lithuania on March 26 as they look to extend their lead at the top of their World Cup 2018 qualifying group, in which they sit two points ahead of second-place Slovenia after four games.
The Three Lions were embarrassed by Iceland at Euro 2016 as they were knocked out at the last-16 stage but have gone five games unbeaten since that 2-1 defeat.
Jermain Defoe, who hasn't featured for his country since 2013, is in line to make his return against Germany, with the likes of Jake Livermore, James Ward-Prowse and Nathan Redmond also selected in the squad.