A toe injury forced Reus to miss the world champions' previous qualifiers against Poland and Scotland last month, where a pair of victories left Joachim Low's men top of the Group D standings - two points above Poland.
If Germany avoid defeat against Ireland in Dublin on October 8 they will secure a place at next year's finals in France before hosting Georgia in Leipzig three days later.
Low said: "Our goal is to win the two games against Ireland and Georgia and to qualify as group winners for the European Championship in France.
"I have great confidence in the players. These players are regularly called upon with their clubs in the league and at European level, they have a good rhythm."
On Leno's selection, Germany goalkeeping coach Andreas Kopke added: "I have already said that behind Manuel Neuer on the position of the goalkeeper we have several candidates in mind.
"I told Ron-Robert Zieler we know what he can do and what we have in him. Bernd Leno has earned this nomination through consistent and good [performances] at Bayer Leverkusen."
Defenders: Jerome Boateng (Bayern Munich), Emre Can (Liverpool), Matthias Ginter (Borussia Dortmund), Jonas Hector (Cologne), Mats Hummels (Borussia Dortmund), Shkodran Mustafi (Valencia), Sebastian Rudy (Hoffenheim)
Midfielders: Karim Ballarabi (Bayer Leverkusen), Ilkay Gundogan (Borussia Dortmund), Christoph Kramer (Bayer Leverkusen), Toni Kroos (Real Madrid), Thomas Muller (Bayern Munich), Mesut Ozil (Arsenal), Bastian Schweinsteiger (Manchester United).