The Yankees did not announce who would take Ayala's spot on the roster.
Manager Joe Girardi announced the developments following the postponement of Tuesday's game between the Yankees and the Orioles in the Bronx.
Prior to the washout, Feliciano said he felt good after his first game of catch in 14 days. But an examination by the doctor will require an MRI on Wednesday.
"Wasn't that bad," Feliciano said of how he felt. "It didn't feel like me. My arm was loose. It wasn't tight. It wasn't me. I just don't feel like it was me.
"I was so happy to play catch today. We'll see what happens with the MRI and go on from there."
"It's a concern," Girardi said. "We were hoping after these two weeks, we'd be able to take the next step and then the next step, and we're just not there yet."
In Feliciano's absence, the Yankees have carried Boone Logan as their lone left-handed reliever. Damaso Marte, another southpaw, is on the 60-day disabled list after surgery to correct a torn labrum in his shoulder.
"You go on at the pace that you can go at, but you can't rush it, because we don't want any setbacks," Girardi said before Tuesday's game was rained out. "So I can't tell you exactly when he is going to be back. He has a ways to go in the sense of hurdles he has to clear. He has to be able to play catch, he has to be able to play long-toss, he has to be able to throw on flat ground, bullpen, games and he has to be able to recover."
Ayala has pitched five innings in three appearances this season.
"Instead of saying he might be back in four or five days, we're just going to be smart and make sure we have enough pitching," Girardi said.
The Yankees could consider bringing up left-hander Steve Garrison, a Minor League starter who earned consideration for the bullpen in Spring Training.