Chamberlain suffered an open dislocation of his right ankle while playing with his 5-year-old son on a trampoline on Thursday in Tampa, where he was continuing his rehabilitation after Tommy John surgery last June.
Chamberlain will be in a non-weight bearing hard cast for six weeks, and a walking boot after that for an undetermined amount of time, Yankees general manager Brian Cashman said.
A CT scan taken Friday showed no microfractures, so no further surgery is necessary.
"Now he's just gotta heal," Girardi said.
There is no official timetable for Chamberlain's return.
Cashman visited Chamberlain in the hospital on Friday afternoon.
"He was hopeful that he could be back on the mound by July, is what he said that they had told him," Cashman said. "That's what he told me the doctors are telling him."
When asked about the right-hander's hope to be back on a mound in July, Girardi said, "Well, I mean if you're talking July 1 to July 15 to July 25, there's a big difference there. He's gonna be a in a cast for I think six weeks, and then you start rehabbing.
"Six weeks is gonna take you to, what, May 10? So I don't necessarily think that that's out of the question."
There has been speculation this could be a career-threatening injury for the 26-year-old former phenom. But Girardi remains hopeful Chamberlain will pitch in pinstripes again.
"I have a lot of faith in the way that Joba goes about his business and rehabs, what we've seen his pain threshold is, his ability to come back," Girardi said. "You look at the elbow, and he was ahead of most people's time frame.
"No one knows exactly how a person's body's gonna heal. But I have faith that he's gonna heal and we're gonna have him back."