Context. Amongst the ≈5 × 10⁵ sources identified as variable stars in Gaia Data Release 2 (DR2), 26% are rotational modulation variable candidates of the BY Dra class. Gaia DR2 provides their multi-band (G, G_BP, and G_RP) photometric time series collected by the European Space Agency spacecraft Gaia during the first 22 months of operations as well as the essential parameters related to their flux modulation induced by surface inhomogeneities and rotation. Aims. We developed methods to identify the BY Dra variable candidates and to infer their variability parameters. Methods. BY Dra candidates were pre-selected from their position in the Hertzsprung–Russel diagram, built from Gaia parallaxes, G magnitudes, and (G_BP − G_RP) colours. Since the time evolution of the stellar active region can disrupt the coherence of the signal, segments not much longer than their expected evolution timescale were extracted from the entire photometric time series, and period search algorithms were applied to each segment. For the Gaia DR2, we selected sources with similar periods in at least two segments as candidate BY Dra variables. Results were further filtered considering the time-series phase coverage and the expected approximate light-curve shape. Results. Gaia DR2 includes rotational periods and modulation amplitudes of 147 535 BY Dra candidates. The data unveil the existence of two populations with distinctive period and amplitude distributions. The sample covers 38% of the whole sky when divided into bins (HEALPix) of ≈0.84 square degrees, and we estimate that this represents 0.7–5% of all BY Dra stars potentially detectable with Gaia. Conclusions. The preliminary data contained in Gaia DR2 illustrate the vast and unique information that the mission is going to provide on stellar rotation and magnetic activity. This information, complemented by the exquisite Gaia parallaxes, proper motions, and astrophysical parameters, is opening new and unique perspectives for our understanding of the evolution of stellar angular momentum and dynamo action.