The team did not specify when he sustained the injury.
An MRI performed on Monday revealed the labrum tear, and Cordero, who has been rehabbing in Viera, Fla., will fly out to his native California on Thursday to visit Dr. Lewis Yocum. Yocum will look at another MRI and decide whether Cordero will have surgery -- the likely scenario.
"I had a bullpen [session] on Thursday and I didn't feel comfortable, and I said something about it," Cordero said when reached by phone on Monday. "When I came off the [disabled list the first time], the shoulder was a little sore, but it was nothing.
"No pitcher gets away with [being healthy his entire career]. It's just my turn. It's better to get this fixed now."
Cordero is one of six players currently on the disabled list for the Nationals. Bowden went to visit Cordero in Viera last Monday, when the right-hander started to throw off the mound again and said that he was in the best shape of his life. At that point, Cordero was rehabbing a torn muscle in the back of the same shoulder, and the team was hopeful he would be activated after the All-Star break.
Cordero said the muscle is fine, but he missed the first part of the season with shoulder tendinitis, which affected his velocity and likely led to this injury.
"It's really unfortunate at this time because we have missed him so bad this first half," manager Manny Acta said. "We were looking forward to him coming back the second half to stabilize our bullpen better.
"But it's just another injury for us."
Jon Rauch, acting as the Nationals' closer in Cordero's place, has gone 4-1 with a 2.18 ERA and a career-high 16 saves this season.
Cordero hasn't pitched much this year. The 26-year-old right-hander originally went on the DL on April 4, retroactive to March 27, but after being activated on April 12, he was put back on the DL on May 2 and hasn't returned. This season, Cordero has appeared in just six games, posting a 2.08 ERA with no saves.
"It's very difficult getting through all that rehab," said Nationals pitching coach Randy St. Claire, who estimated a 12- to 18-month recovery period. "It's a lot of work, a lot of time and usually not a lot to look forward to.
"He probably was [throwing in pain]. He said it didn't hurt, but the thing with him was, he wasn't throwing one or two mph [slower]. He was like 10 mph off."
Alden Gonzalez is an associate reporter for MLB.com. Bill Ladson, a reporter for MLB.com, contributed to this story. This story was not subject to the approval of Major League Baseball or its clubs.