We present a study of the photometric variability of spectroscopically confirmed supergiants in NGC 300, comprising 28 epochs extending over a period of 5 months. We find 15 clearly photometrically variable blue supergiants in a sample of nearly 70 such stars, showing maximum light amplitudes ranging from 0.08 to 0.23 mag in the V band, and one variable red supergiant. We show their light curves and determine semiperiods for two A2 Ia stars. Assuming that the observed changes correspond to similar variations in bolometric luminosity, we test for the influence of this variability on the flux-weighted gravity-luminosity relationship and find a negligible effect, showing that the calibration of this relationship, which has the potential to measure extragalactic distances at the Cepheid accuracy level, is not affected by stellar photometric variability in any significant way. Based on observations obtained with the 2.2 m ESO/MPI telescope at the European Southern Observatory as part of proposal 163.N-0210.