Murphy was promoted to Triple-A Charlotte on Sunday, James Fegan of SoxMachine.com reports.
Murphy will make his way to Charlotte after posting a 3.99 ERA and 1.19 WHIP with 21 strikeouts over 29.1 innings in five starts with Double-A Birmingham this season. The southpaw is now just one step away from potentially making his major-league debut down the road this season.