General manager Brian Cashman said in a conference call Thursday that Tanaka could return in six weeks but didn't rule out the possibility of Tommy John surgery if the right-hander doesn't respond to a rehab program.
On Friday, the Yankees' ace released a statement on his injury, saying he "will be going through some treatment and rehab on my injured elbow over the next several weeks."
"I give everything I have every time I take the ball. With that, I also know that there will always be a risk of injury when playing this game that I love. Right now I feel that the most important thing for me is to keep my head up, remain focused on the task at hand and devote all my energy into healing the injury in order to come back strong," he said.
"I want to apologize to the Yankees organization, my teammates and our fans for not being able to help during this time. I accept this injury as a challenge, but I promise to do everything I can to overcome this setback and return to the mound as soon as possible."
Tanaka was placed on the 15-day disabled list Wednesday and had an MRI in New York, one day after his worst major league outing. He flew to Seattle on Thursday.
"I think it shows you how much he loves the game and how much he loves pitching and the responsibility he puts on his shoulders of being out there every fifth, sixth day and performing at a high level," Yankees manager Joe Girardi told reporters. "And I'm sure it's extremely difficult for him right now. It's the first time he's probably been through something of this magnitude."
Cashman said Thursday that Tanaka saw three doctors, including Yankees head physician Dr. Christopher Ahmad, and all three agreed that a six-week rehab program was the best option at this time.
Tanaka, who is tied for the major league lead with 12 wins, allowed five runs and 10 hits -- both career highs -- over 6 2/3 innings Tuesday night in a 5-3 loss to the Indians.
The All-Star is 12-4 with a 2.51 ERA in 18 starts but has lost three of his past four outings. The injury is a huge blow to a battered Yankees rotation that already was missing CC Sabathia, Ivan Nova and Michael Pineda to injuries. Tanaka had been a stabilizing ace in his first season since arriving from Japan.
Mets ace Matt Harvey initially tried to rehab a partial tear of his ulnar collateral ligament last year before ultimately opting for Tommy John surgery. Harvey has been sidelined all season, but his rehabilitation appears to be going well.
"When it comes time to trying to work through it, it's a personal decision. Going down and having Tommy John surgery is a personal decision in itself. Everybody is different. No one is saying that he can't rehab and be completely fine and never have an issue again. For me, personally, it was a mental thing. It was something I didn't want to continue thinking about," Harvey said Thursday night in New York.
"I would tell him to just go with what you feel. I didn't listen to anybody. I went off of my personal feelings. It's your body that you want to throw with again. If you want to go out and try not to have it, and your mind is set to that and you're 100 percent committed to that, then more power to you. If it's the other way around, then go get it done."
The Associated Press contributed to this report.