We report on the design, fabrication, and demonstration of the operation of a latching (nonvolatile) low-loss microwave switch at 4.2 K and 40 mK using the phase-change material germanium telluride (GeTe) as the switching element. The single-pole double-throw (SPDT) series–shunt switch has a single RF input and two selectable RF outputs. An insertion loss of less than 1 dB from DC to 10 GHz was demonstrated, with virtually identical performance across 5000 switching cycles at 40 mK. We have also characterized the resistance of the GeTe thin-film material used in the fabrication of the SPDT switch from room temperature down to 11 mK. While bulk GeTe is known to become superconducting below 1 K, these GeTe films showed no detectable superconducting transition, resulting in a switch with finite on-state DC resistance. Given the wide range of phase-change material candidates reported in the literature and prior evidence of superconductivity, this demonstration paves the way for future development of a near-ideal switch which could have zero on-state DC resistance at cryogenic temperatures.