"My guess is he probably is going to have to have surgery," Girardi said.
Girardi said Chamberlain will likely have Tommy John surgery.
"With Tommy John, you are talking [being out] 10 to 14 months," general manager Brian Cashman said.
"This sucks," Chamberlain said. "There's no way to sugarcoat it. It's something I didn't expect with no pain. The most frustrating part is not being there for the team. [But] everything happens for a reason. I'll come back and be even stronger."
Surprisingly, Chamberlain said he feels "no pain" and has "no idea" how the injury occurred. But he felt tightness after throwing long-toss on Tuesday and went in for an MRI on Wednesday, which revealed he had a strained flexor tendon.
Chamberlain was placed on the 15-day disabled list on Wednesday, but a dye contrast MRI on Thursday morning revealed that the injury was more significant.
"I was just trying to get out of there before I broke down," Chamberlain said of his reaction to the devastating news. "I shed a couple tears. [But] you can't let it beat you. You gotta get stronger and get better."
Chamberlain's MRI results will be sent to renowned orthopedic surgeon Dr. James Andrews, where it will be determined whether or not he needs to undergo Tommy John surgery.
"This is a surgery that a lot of people have, and people understand that you can come back from this. Surgery is just a third of it. The rehab is two-thirds of what's going on. So that's an important part and the most important part," Chamberlain said Friday. "[Andrews] has [performed Tommy John] a bunch of times, so I'm confident he's gonna do a good job, and the rest is on me and making sure I get to where I can be and get even stronger.
"It is what it is. There's no thinking about it. I'm just gonna take it one day at a time. I've just gotta make the most of it and try to come back stronger."
Soriano, who was signed for three years and $35 million this offseason, has been a major disappointment and is on the disabled list with right elbow inflammation.
Soriano has not started throwing yet, Girardi said, and is not close to returning. David Robertson will be the Yankees eighth-inning man for now, Girardi said.
Girardi said the team is "confused" by Chamberlain's injury because the reliever has not experienced any of the typical symptoms of pitchers who need Tommy John surgery.
"He said (Wednesday) was a normal long-toss for him so it really has us all kind of scratching our head," Girardi said on Thursday. "When you talk about the symptoms that someone has when they hurt that ligament, Joba doesn't have them."
When asked about the extent of the injury on Wednesday, Chamberlain said: "If you asked me to pitch today, I would tell you I could pitch today."
On Thursday, Girardi added, "He has no idea when this happened."
Before the latest diagnosis, the Yankees thought Chamberlain would sit two weeks to a month and then start a throwing program, Girardi said.
Chamberlain had emerged as the team's setup man in the absence of right-hander Soriano and in 28 2/3 innings had 12 holds and a 2.83 ERA.
The Yankees placed rules on Chamberlain to limit his innings in 2009, when he was used as a starter.
"If there were no 'Joba Rules' in place, could it have possibly happened earlier? I don't know," Girardi said. "There's no exact science because everybody is different."
Andrew Marchand covers the Yankees for ESPNNewYork.com. ESPNNewYork.com's Michael Mazzeo and Ian Begley contributed to this report.