Royals general manager Dayton Moore said on the Royals Radio Network that he didn't expect Minor to contribute on the Major League level this season.
"We're not too optimistic he's going to be in a position to help us this year," Moore said, "based on some news we got after the game [Friday] night."
Minor, 28, signed a two-year $7.25 million deal prior to the season. He was recovering from labrum surgery last year.
Jeffrey Flanagan has covered the Royals since 1991, and for MLB.com since 2015. Follow him on Twitter @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.