Manager Trey Hillman was asked whether he was concerned that Parrish might have to go on the disabled list.
"It's a concern to the point that it's been sore for a few days," Hillman said. "We'll see what the next few days brings."
Parrish made the Royals' roster in Spring Training after missing all of 2009 after undergoing shoulder surgery. He has pitched in nine games with a 1-1 record and a 3.00 ERA over six innings.