The White Sox outrighted Murfee to Triple-A Charlotte on Tuesday, Scott Merkin of MLB.com reports.
Murfee lost his place on the major-league roster Sunday after turning in a 7.82 ERA over 12.2 innings, and he has now also lost his 40-man spot. He'll stick with the organization as bullpen depth for the Knights, though he'd likely need to show significant improvement to get another shot in Chicago.