Wawrinka, making his 13th appearance at the tournament in his native country, was derailed in three sets by Zverev 6-2, 5-7, 6-1.
Zverev broke Wawrinka's serve six times in becoming the first qualifier to reach the tournament semifinals since Marcos Baghdatis in 2005.
"It was tough for me to find my game, to move well enough and to do what I needed to do," Wawrinka said.
Zverev, who beat an opponent ranked in the top 10 for the first time since 2010, will take on Croatia's Marin Cilic in the semifinals.
The fourth-seeded Cilic breezed to a 6-3, 6-3 victory over Spain's Marcel Granollers in his quarterfinal match.
No. 3 seed Kei Nishikori advanced to the semifinals with a 7-5, 6-4 victory over Argentina's Juan Martin del Potro, a two-time champion in this event.
Nishikori, seeking to reach his fifth final of the year, reversed a dismal track record against del Potro, who had won all four previous meetings without even giving up a set to Nishikori.
Awaiting Nishikori in the semis is Gilles Muller, who lost the opening set and needed a stunning comeback in a 6-7 (4), 6-4, 7-6 (3) victory over another Argentine, Federico Delbonis.
Muller trailed 5-3 with Delbonis serving for the match before winning the next three games and eventually prevailing in the tiebreaker. Muller, bidding for his third final of the year, has dropped both career matchups against Nishikori.