Rivera, 41, said that he started to feel the soreness after his blown save on Sunday against the Mets at Citi Field.
"It's improving. Hopefully [Tuesday] I'll be ready to pitch," Rivera said. "I'm not concerned about it, I can tell you that. It's things that happen."
Dave Robertson would have served as New York's closer in a save situation on Monday. Yankees manager Joe Girardi said that he did not know of any tests that had been scheduled for Rivera.
"He's had issues that he gets worked on before, and he always seems to bounce back," Girardi said. "If it goes on for a few days, yes, then you get a little bit more concerned. Mo has had to fight through things to stay around this long. That's what he does."
With both Rivera and Luis Ayala unavailable after the latter had pitched in three of the last four games, Girardi said that he tried to push starter A.J. Burnett through seven innings, and might have even gone to the eighth with him.
Burnett surrendered four runs in the seventh to the Indians and suffered a 6-3 defeat.