Bauer, selected third overall in the 2011 Draft, was optioned to Double-A Mobile, where he made four starts at the end of last season before helping the BayBears capture the Southern League championship.
Despite a strong spring that saw the former UCLA star go 1-0 with a 3.60 ERA, nine strikeouts and one walk over 10 innings, Bauer could not supplant Josh Collmenter for the final spot in the D-Backs' rotation.
Diamondbacks manager Kirk Gibson praised Bauer, telling MLB.com he thought he was "very unique."
"He had a great spring for us," Gibson said. "We really enjoyed our time with him as well."
Gibson also downplayed the decision to give the right-hander more time in the Minors while keeping fellow prospects Tyler Skaggs and Patrick Corbin with the Major League club for the time being.
"I'm not going to go into all the reasons we decided to do it that way," Gibson said. "We knew we had to send two of the young kids down and we made the decision that those were the guys that would go down. Don't read too much into it, I guess, is what I'm saying."
Arenado is probably headed for Double-A Tulsa after teeing off on California League pitching last year. He hit .298 with 20 homers and 122 RBIs in his third season since being taken in the second round of the 2009 Draft.
The 20-year-old third baseman went on to claim MVP honors in the elite Arizona Fall League, then batted .192 with five RBIs in 26 at-bats this spring. With Casey Blake injured and Chris Nelson and Jordan Pacheco battling for the starting job in Colorado, Arenado will bide his time in the Texas League.