There was no timetable for Chamberlain's return. The team did not say whether the 26-year-old pitcher was using the trampoline equipment when he was injured Thursday.
The accident at a play area came two weeks after All-Star setup man David Robertson hurt himself moving boxes at home.
Yankees general manager Brian Cashman said Friday that Chamberlain had surgery and would be hospitalized at least a few days. The 6-foot-2, 240-pound righty was working his way back from elbow ligament replacement surgery and wasn't expected to return until June or July.
Asked Friday if this could threaten Chamberlain's career, Cashman said: "I'm not in position to say. Right now it's too early for that. He's in very good hands. He's a healer. He's a tough guy."
Bone broke through the skin during the dislocation. Chamberlain was scheduled for an MRI exam and CT scan Friday.
"My guess is he landed funny," Yankees manager Joe Girardi said.
Girardi said he spent about 30 minutes with Chamberlain at the hospital Friday morning that both of them were "a little emotional."
"I wanted to see how he was doing. You know it's crushing. I just told him, we're going to be here for him, we're going to get you through this and we're going to get you back on the mound. But you're going to go through some difficult times," Girardi said.
"You can only look forward. You've got to look forward. You can't look at 'what if?'" he said. "You can see the disappointment, there's no doubt that."
Earlier this month, Robertson stumbled on the stairs of his home in St. Petersburg while moving empty boxes for recycling. The Yankees' fears of a serious injury were abated when Robertson was diagnosed with a bone bruise.
And once it became clear Robertson's injury was minor, his teammates let him have it. Among those in the clubhouse weighing in with sarcastic cracks about carrying boxes was Chamberlain himself. Chamberlain often is like a big kid himself, joking with teammates and playing around.
But there was little humour coming out of the Yankees' camp Friday. The mood in the clubhouse was sombre, and Cashman seemed shaken as he met with reporters. He even acknowledged at the end of the media session that he was rambling.
"He's facing a lot right now," Cashman said. "I can't tell you, really, anything more than something unfortunate happened. We're in the very early information side of this thing."
In January, Chamberlain agreed to a one-year contract for $1,675,000, up from $1.4 million last year. The deal was not guaranteed. Cashman said Friday it's not the right time to talk about Chamberlain's contract status.
As to whether this falls in the category of unacceptable off-the-field injuries, Girardi said: "I don't want to get into that now. What I want to talk about is getting him better and being there for this kid. He's going through a lot."
Cashman said Chamberlain's son was not hurt. The boy began kindergarten last year and Chamberlain often tweets about how proud he is of his son's hockey.
Chamberlain went 2-0 with a 2.83 ERA in 27 relief appearances last season before elbow surgery June 16. Now, another setback
"I feel extremely bad for him," Yankees captain Derek Jeter said. "He's worked hard to get his arm back in shape. A fluke accident. I feel extremely bad for him. He's got to be disappointed. I feel terrible for him."
Chamberlain was his usual playful self inside the Yankees' clubhouse Thursday and had a bullpen session set for Friday.
"From the baseball stuff, he was doing great," Cashman said. "I feel bad because I know how much he loves his game, and how much he was looking forward to coming back ahead of schedule. It's clearly derailed that, but what more does that mean, I don't know. A lot of things must be running through his mind."
Chamberlain has had an up-and-down career since joining the team in August 2007. He started out 2-0 with an 0.38 ERA in 19 relief appearances.
Chamberlain later inspired the "Joba Rules" that governed how much he would pitch, with the Yankees wary of overusing him while deciding whether he would be a starter, setup man or closer-in-waiting behind Mariano Rivera.