Bauer was Arizona's top selection (third overall) in the 2011 First-Year Player Draft.
The right-hander was impressive in big league camp during Spring Training and has been dominating Southern League hitters.
In eight starts for Mobile, Bauer was 7-1 with a 1.68 ERA and he allowed just 33 hits in 48 1/3 innings, while striking out 60 batters.
"I wouldn't say he completely overmatched Double-A," D-backs GM Kevin Towers said. "But I think if you look at his numbers, we wanted to put him in an environment where he probably was facing a little better competition, a little more of a veteran hitter, smaller ballpark where it's going to be a little more difficult for him."
Bauer drew lots of attention during the spring for his unique pregame routine, which includes long tossing almost from foul pole to foul pole.