Penny should be out no more than two weeks, Dodgers manager Joe Torre said. He'll be eligible to return June 30 and will begin throwing later this week.
In a corresponding roster move, left-hander Eric Stults was called up from Triple-A Las Vegas and will start Thursday in the series finale against the Reds in Cincinnati.
Derek Lowe, who was originally slated to pitch Thursday, was moved up to Wednesday after Hiroki Kuroda was sent home from Cincinnati on Tuesday with soreness in his right shoulder.
The move, retroactive to Sunday, comes after Penny underwent an MRI exam Monday in Los Angeles. It revealed no structural damage.
Penny had complained of discomfort in his shoulder for more than a month without missing a start, but the pain worsened during pregame warmups in his last start on Saturday against Detroit.
"Structurally, he's fine," Torre said. "The thing that's tricked us all is when you look up there and see his velocity numbers -- they seem to be pretty consistent. At times, he looked really good. But again, his inconsistency certainly matches up with the fact that he's had this discomfort. Some days have been better than others."
Penny made the All-Star team in 2007 when he finished 16-4 with a 3.03 ERA, but has been inconsistent since. He's 5-9 with a 5.88 ERA through 14 starts this season.
Stults, who is 5-6 with a 3.59 ERA through 14 starts at Las Vegas this season, will be making his season debut. He made five starts and 12 appearances for the Dodgers in 2007 and two starts in six appearances in 2006.
"I was throwing well down there, and I knew if I kept throwing well, something would happen," Stults said. "All in all, it's easy to go out there in Triple-A or wherever you are when you're throwing well and having fun. You've got to believe that I'd have the opportunity. You just never know -- every year that a team loses so many guys. You've got to think that if you're throwing well, the opportunity might present itself."
Stults, who led Las Vegas in innings pitched (82 2/3) and strikeouts (67), got news of his promotion Monday night after a game in Salt Lake City. He flew into Cincinnati on Tuesday morning.
Stults said he believes he's a different pitcher than he was a season ago, mainly because of his ability to be aggressive and get ahead of hitters early in the count.
"My focus this year was to throw every pitch with confidence and just be aggressive," Stults said. "You have a tendency in that league to try and miss bats, and you can't do that because you'll find yourself behind 2-0 and then you have to throw strikes. The key for me was throwing strike one and being aggressive. That's what I was going most outings, and it was getting me some success."
Brandon Harris is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.