Context. In galaxies, the flattening of the spectrum at low radio frequencies below 300 MHz has been the subject of some debate. A turnover at low frequencies could be caused by multiple physical processes, which can yield new insights into the properties of the ionised gas in the interstellar medium. Aims. We investigate the existence and nature of the low-frequency turnover in the H II regions of M 101. Methods. We study the nearby galaxy M 101 using the LOw Frequency ARray (LOFAR) at frequencies of 54 and 144 MHz, Apertif at 1370 MHz, and published combined map from the Very Large Array (VLA) and Effelesberg telescope at 4850 MHz. Results. The spectral index between 54 and 144 MHz is inverted at the centres of H II regions. We find a significant low-frequency flattening at the centres of five out of six H II regions that we selected for this study. Conclusions. The low frequency flattening in H II regions of M 101 can be explained with two different free-free absorption models. The flattening is localised in a region smaller than 1.5 kpc and can only be detected with high resolution (better than 45″). The detection of low frequency flattening has important consequences for using radio continuum observations below 100 MHz to measure extinction-free star-formation rates.