Chamberlain will be off 10-14 days and then start a throwing program afterward, manager Joe Girardi said. Chamberlain is expected to be out for at least three weeks.
An MRI on Wednesday revealed the injury. Chamberlain said he is going to get a second MRI on Thursday to make sure the damage is not more severe.
Right-hander Hector Noesi has been sent down to Triple-A Scranton, while the Yankees brought up pitchers Amauri Sanit and Jeff Marquez, who was claimed off waivers from the White Sox, to fill those roster spots.
"I played long toss and assumed it was going to be fine," said Chamberlain, who added he doesn't think the injury is "serious." "And then as soon as I was done it became tight and it was something that was a little bit awkward for me. I kind of felt it a little bit, but (it was) nothing to pay attention to. And finally I was like let's get it figured out and see what it is instead of worrying about it and (trying to) compensate and (hurting) something else. I thought I'd say something.
"If you asked me to pitch today, I would tell you I could pitch today."
Chamberlain had emerged as the team's setup man in the absence of right-hander Rafael Soriano. In 28 2/3 innings, Chamberlain has compiled 12 holds and a 2.83 ERA.
"It sucks for me, but I could care less about myself," Chamberlain said. "Just the fact that I'm not gonna be out here helping my teammates. Not being there and the seventh and the eighth inning for these guys."
Girardi said that Chamberlain's injury had nothing to do with his 35-pitch outing in Los Angeles on June 5. That's the last time Chamberlain pitched. Girardi added that he had no regrets using Chamberlain even though the reliever was pitching in admitted discomfort.
"His arm has been a little tender in the last couple of weeks and we've been careful with him," the manager said.
"Guys who are able to shut down teams in late-inning situations are really hard to replace," Girardi said. "Everyone's looking for them. When you have two of them go down, it's difficult. But guys have to step up."
The Yankees decided to send Noesi down because he would not be available for the next four days after throwing six-plus innings on Tuesday night -- the longest outing by a Yankee reliever since 2007.
Girardi praised Noesi's efforts, referring to him as a future starting pitcher.
"He did everything that we could have asked of him," the Yankee manager said.
Ian Begley and Mike Mazzeo are regular contributors to ESPNNewYork.com.