Putz, who was placed on the DL on May 4 with tightness in his right forearm, had made two rehab appearances for Reno late last week.
To make room on the roster, the D-backs designated right-hander Trevor Cahill for assignment and placed third baseman Eric Chavez on the DL with a sprained left knee.
Chavez has been battling the knee issue since Spring Training and it finally reached the point where the club had no choice but to DL him.
The moves leave the D-backs with 13 pitchers and 12 position players rather than the usual 13 position players and 12 pitchers.
While admitting it's not an ideal situation because it leaves him short a man on the bench, D-backs manager Kirk Gibson said it was necessary given the way the bullpen has been taxed recently.
Steve Gilbert is a reporter for MLB.com. Read his blog, Inside the D-backs, and follow him on Twitter @SteveGilbertMLB. This story was not subject to the approval of Major League Baseball or its clubs.