Our simultaneous three-colour (BVR) polarimetric observations of the low-mass black hole X-ray binary V404 Cyg show a small but statistically significant change of polarization degree (Δp ∼ 1 per cent) between the outburst in 2015 June and the quiescence. The polarization of V404 Cyg in the quiescent state agrees within the errors with that of the visually close (1.4 arcsec) companion (pR = 7.3 ± 0.1 per cent), indicating that it is predominantly of interstellar origin. The polarization pattern of the surrounding field stars supports this conclusion. From the observed variable polarization during the outburst, we show that the polarization degree of the intrinsic component peaks in the V band, pV = 1.1 ± 0.1 per cent, at the polarization position angle of θV = -7° ± 2°, which is consistent in all three passbands. We detect significant variations in the position angle of the intrinsic polarization in the R band from -30° to ∼0° during the outburst peak. The observed wavelength dependence of the intrinsic polarization does not support non-thermal synchrotron emission from a jet as a plausible mechanism, but it is in better agreement with the combined effect of electron (Thomson) scattering and absorption in a flattened plasma envelope or outflow surrounding the illuminating source. Alternatively, the polarization signal can be produced by scattering of the disc radiation in a mildly relativistic polar outflow. The position angle of the intrinsic polarization, nearly parallel to the jet direction (i.e. perpendicular to the accretion disc plane), is in agreement with these interpretations.