Nunez, a right-hander, has a 3-1 record with a 1.71 ERA. His only loss came Tuesday night when he allowed the go-ahead run in the 12th inning against the Twins. He wasn't available to pitch Wednesday night.
Musser is 0-4 with a 3.07 ERA and six saves for Omaha so far this season.
Nunez isn't the only Royal bothered by physical ailments. David DeJesus was taken out in the eighth inning after breaking out in hives.
"He couldn't stop it and had to get off the field," manager Trey Hillman said. "He's had it on and off the last four or five days. He's been fighting it."
Mark Dent is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.