Schultz, who was selected with the 300th overall pick in the 2014 First-Year Player Draft, has mostly pitched in relief for the Beavers.
But facing an elimination game against UC-Irvine last weekend, Schultz was pressed into duty as a starter.
The 22-year-old responded with a two-hit shutout that helped the Beavers stave off elimination for one more day.
Schultz was the fifth Oregon State player to be taken in this year's Draft. Michael Conforto, Jace Fry, Dylan Davis and Ben Wetzler were also drafted.
Schultz was 7-2 with a 1.61 ERA this past season. He was taken by the Marlins in the 17th round of last year's Draft, but elected to return for his senior season.
The D-backs will give Schultz the chance to start before moving him to the bullpen.
"Big-bodied guy who has starter stuff," D-backs scouting director Ray Montgomery said of Schultz, who was scouted by Donnie Reynolds.
Schultz has a 3-year-old daughter, Madison.
The Draft concludes on Saturday, with exclusive coverage of Rounds 11-40 beginning on MLB.com at 10 a.m. MST.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. Adam Lichtenstein is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.