"We know he's not going to be back anytime soon," D-backs manager Kirk Gibson said.
Putz was forced to leave Tuesday night's game against the Dodgers after walking the only batter he faced on four pitches. After the second pitch, he felt stiffness in his elbow, and after the fourth pitch he was visibly clenching and unclenching his fist and shaking his arm.
In addition to the stiffness in the elbow Putz felt "zinging" through his fingers.
Gibson said setup man Heath Bell would get the first crack at the closer job in Putz's absence, and Bell was immediately tested Wednesday night. He worked around a leadoff double before closing the D-backs' 3-2 win over the Dodgers for his third save of the season.
"I think we're going to miss J.J.," Bell said. "He's kind of our captain down there, our leader."
In 14 games this season, Putz is 2-1 with five saves in nine opportunities and a 4.26 ERA.
To take Putz's spot on the roster, the D-backs recalled right-hander Will Harris from Triple-A Reno.
Harris went to Spring Training with the Rockies and was claimed on waivers by the A's on April 3. Three days later the D-backs claimed him from the A's and sent him to Triple-A Reno.
"This is where my goal is to be," Harris said. "Obviously when I was claimed by Arizona I was really excited, it's a good opportunity. I'm just glad it all worked out and here for however long it may be and hopefully I can just help the team win some games."
In 12 relief appearances for Reno he had two saves and a 4.63 ERA.
Gibson said he planned on easing Harris into action probably in the middle innings.