ABSTRACT Radio galaxies are linearly polarized – an important property that allows us to infer the properties of the magnetic field of the source and its environment. However, at low frequencies, Faraday rotation substantially depolarizes the emission, meaning that comparatively few polarized radio galaxies are known at low frequencies. Using the LOFAR Two-metre Sky Survey at 150 MHz and at a resolution of 20 arcsec, we select 342 radio galaxies brighter than 50 mJy and larger than 100 arcsec in angular size, of which 67 are polarized (18 per cent detection fraction). These are predominantly Fanaroff–Riley type II sources. The detection fraction increases with total flux density, and exceeds 50 per cent for sources brighter than 1 Jy. We compare the sources in our sample detected by the LOw Frequency ARray (LOFAR) to those also detected in NRAO VLA Sky Survey at 1400 MHz, and find that our selection bias towards bright radio galaxies drives a tendency for sources depolarized between 1400 and 150 MHz to have flatter spectra over that frequency range than those that remain polarized at 150 MHz. By comparing observed rotation measures with an analytic model, we find that we are preferentially sensitive to sources in low-mass environments. We also infer that sources with one polarized hotspot are inclined by a small angle to the line of sight, while sources with hotspots in both lobes lie in the plane of the sky. We conclude that low-frequency polarization in radio galaxies is related to a combination of environment, flux density, and jet orientation.