Cashman said the accident happened Thursday afternoon while Chamberlain and his son were at a Tampa-area spot that has trampoline equipment. The team did not say whether the 6-foot-2, 240-pound pitcher was using any of the equipment.
Bone broke through the skin during the dislocation. Chamberlain is scheduled for an MRI exam and CT scan Friday. He is already returning from elbow ligament replacement surgery.
When asked if the injury could threaten the career of the 26-year-old reliever, 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."
Chamberlain went 2-0 with a 2.83 ERA in 27 relief appearances last season before elbow surgery on June 16. He had been expected to rejoin the Yankees this season, possibly before the All-Star break.
"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."
Cashman said Chamberlain's son was not hurt.
Yankees manager Joe Girardi visited Chamberlain on Friday. Cashman, who was informed about the injury Thursday night while the Yankees were playing a night game in Fort Myers against Boston. He was planning to stop at the hospital later Friday.