Dustin Nippert filled in for Owings, who is expected to be able to make his next start Saturday against the Cubs in Mesa.
"He's had some stiffness throwing the last several days, so rather than having him go out there with some stiffness and some soreness we're just going to bump him back to his next start," D-backs manager Bob Melvin said.
The soreness is not related to Owings swinging the bat as a designated hitter Sunday, but rather something he's felt for a little while. The right-hander threw 152 2/3 innings as a rookie in 2007.
"The longer you're around in Spring Training you have some soreness, and it's something you've been through, where this might be the first time he's been through that," Melvin said.
Owings said that the soreness was in the back of his shoulder and that he has experienced it before in his career.
"That's why I'm not concerned about it," he said. "I think pitchers go through it from time to time, whether it's early, middle or late in the season. We decided to nip it right now so I'll be ready to go here pretty soon."
In the groove: Right fielder Justin Upton was just 1-for-6 this spring before going 3-for-3 against the White Sox on Sunday in Hermosillo, Mexico.
"It's all about timing, and Spring Training is where we find it," Upton said. "It was just one of those days where it happened to be on and hopefully it progresses from there. It's tough to get on the field and just jump right into it. Saw some pitches, and I felt like I was seeing the ball well so it was time to start grooving the swing a little bit."
Upton, 20, hit .221 in 43 games after having his contract purchased from Double-A Mobile on Aug. 2 last year.
"Staying on some balls and not pulling out of there a little bit," Melvin said when asked why Upton had success Sunday. "When he lets the ball travel and gets a good look at it, his ability is going to take over."
Speaking of hitting: Chris Young was hitless in his first eight at-bats this spring before he hit a solo homer off Aaron Cook in the third inning Monday.
Young followed that up with a double two innings later.
"C.Y. swung the bat well," Melvin said. "His at-bats in batting practice have been real good, and it's good to see him get a couple of hits out of it. He's got a confident look in his eye. It was good to see him square some balls up today. He's got a chance to have big year."
Command and control: Nippert struggled for the second time this spring and has allowed six earned runs in three innings. The right-hander, who is out of Minor League options and came into camp as the front-runner for the final spot in the bullpen, has struggled with getting his fastball over for strikes.
"Right now, I'm just trying to establish my fastball," he said. "Once I establish that I think my other pitches will come. I'm just not able to throw it for strikes effectively early in counts and I'm getting behind, and then when I am able to throw strikes I'm behind and they are waiting on it."
Nippert has thrown just fastballs, curves and changes so far this spring, but has yet to break out his new slider because he hasn't been ahead enough in the count to do so.
Up next: The D-backs make their first appearance in the Phoenix area Tuesday when they take on the Rangers in Surprise. Ace Brandon Webb will make his second start of the spring. The right-hander tossed two scoreless innings in his first outing. The rest of the Arizona lineup is scheduled to be: Eric Byrnes (lf), Stephen Drew (ss), Conor Jackson (1b), Chris Snyder (c), Upton (rf), Trot Nixon (dh), Alex Romero (cf) and Emilio Bonifacio (2b).
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.