ABSTRACT Mercury–manganese (HgMn) stars are late-B upper main sequence chemically peculiar stars distinguished by large overabundances of heavy elements, slow rotation, and frequent membership in close binary systems. These stars lack strong magnetic fields typical of magnetic Bp stars but occasionally exhibit non-uniform surface distributions of chemical elements. The physical origin and the extent of this spot formation phenomenon remain unknown. Here, we use 2-min cadence light curves of 64 HgMn stars observed by the Transiting Exoplanet Survey Satellite (TESS) during the first 2 yr of its operation to investigate the incidence of rotational modulation and pulsations among HgMn stars. We found rotational variability with amplitudes of 0.1–3 mmag in 84 per cent of the targets, indicating ubiquitous presence of star-spots on HgMn-star surfaces. Rotational period measurements reveal six fast-rotating stars with periods below 1.2 d, including one ultra-fast rotator (HD 14228) with a 0.34-d period. We also identify several HgMn stars showing multiperiodic g-mode pulsations, tidally induced variation and eclipses in binary systems.