"Certainly disappointed for our player, for our organization," Cashman said. "He's been an important piece. We have a tremendously gifted and tough player. We'll see how he responds."
"It is what it is," manager Joe Girardi said. "We're not going to have him for at least six weeks and that's the tough part, but I'm optimistic that we'll have him back."
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.
Cashman said 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.
"If we knew today that the best course of action was Tommy John surgery, despite the name and the amount of the investment, we would be doing Tommy John surgery," Cashman said.
Girardi, looking for any positive sign, said, "Guys have had success doing this and we'll keep our fingers crossed. That gives you reason for optimism that he's going to pitch again for us this year."
Tanaka, who is tied for the major league lead with 12 wins, allowed five runs and 10 hits 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 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.
"We've lost 80 percent of it," Girardi said. "There's really not a whole lot that you can go back and redo. You just gotta go out and find a way."