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 Rivera is 6-5 with a 1.43 ERA and 38 saves in 39 opportunities.
"If we were still playing for something, Mo would still be here," manager Joe Girardi said after New York lost 8-2 to Toronto on Thursday night.
General manager Brian Cashman told reporters before Thursday's game that Rivera had been pitching with discomfort in his shoulder, but didn't tell the team about the injury until after the Yankees were eliminated from postseason play on Tuesday. Cashman said he didn't consider Rivera's condition to be serious, but agreed the right-hander should have an MRI.
"Mo didn't ask to go Wednesday morning," Girardi said. "If there was a huge concern, I think he would have gone Wednesday morning."
Rivera left the team Thursday and flew to New York for the exam. Results have not been made available.
Girardi acknowledged before Thursday's game that Rivera had left the team, but said only that the 38-year-old had complained "his whole body was a little cranky." Girardi said Rivera had returned to New York for end-of-season medical exams, a formality for many players.
Confronted with Cashman's statements after the game, Girardi was defensive.
"I'm telling you what the player told me," Girardi said. "If you don't like it, there's not a whole lot I can do. I'm the manager, I have to answer the questions. I'm answering the questions with the knowledge that I have."
Rivera didn't pitch Wednesday after appearing in four of New York's previous five games.
"I could have pitched him last night if I had to," Girardi said before the game. "Since we were eliminated and he'd pitched four out of five days, I just didn't see a need to do it." | 
