"I can be a small piece to the winning puzzle, but if I'm not fully recovered, I don't want to set back the team more," Rapada said. "If I can't go back-to-back days, I feel like I'd put a lot more strain. I don't feel like I'm very far off, but I don't expect it to be long."
Rapada, 32, was 3-0 with a 2.82 ERA in 70 appearances for New York last season, spanning 38 1/3 innings.
"He'll start the season on the DL. He's not on the DL officially yet," Yankees general manager Brian Cashman said. "In terms of time frame, he's going to need a little bit of April, so he won't be ready. But he'll be ready, I think, pretty quickly."
Rapada's injury could improve the chances of right-handers Cody Eppley or Shawn Kelley making the Opening Day roster, and manager Joe Girardi also said that left-hander Vidal Nuno could be a possibility. Boone Logan is the only lefty locked into the Yankees' bullpen at the moment.
"We're still talking about it," Cashman said. "Obviously, Nuno has opened everybody's eyes and is taking a run at it, trying to force his way on. We'll go with one lefty or we'll go with two."
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. Evan Drellich is a reporter for MLB.com. Follow him on Twitter @EvanDrellich. This story was not subject to the approval of Major League Baseball or its clubs.