"Probably won't see him during this trip," manager Ned Yost said before Sunday's series finale against the Cardinals.
Perez, in his first nine games for Omaha, batted .333 (13-for-39) with two doubles and seven RBIs.
"I don't care what he's hitting, I just check the health of his knee," Yost said. "He feels great after every day. He caught seven innings in the first game of a doubleheader [Saturday] and he'll catch nine innings [Sunday]."
Center fielder Lorenzo Cain, out since the first five games of the season, will begin a new rehab assignment on Monday with Double-A Northwest Arkansas. He was playing for the Naturals getting over a groin strain when a torn hip flexor dealt him a setback.
In addition, catcher Manny Pina, out with knee surgery, is to begin a rehab assignment soon.