On 2015 June 15, the Swift space observatory discovered that the Galactic black hole candidate V404 Cyg was undergoing another active X-ray phase, after 25 years of inactivity. The 12 telescopes of the MASTER Global Robotic Net located at six sites across four continents were the first ground-based observatories to start optical monitoring of the microquasar after its gamma-ray wake up at 18h 34m 09s U.T. on 2015 June 15. In this paper, we report, for the first time, the discovery of variable optical linear polarization, changing by 4%–6% over a timescale of ∼1 hr, on two different epochs. We can conclude that the additional variable polarization arises from the relativistic jet generated by the black hole in V404 Cyg. The polarization variability correlates with optical brightness changes, increasing when the flux decreases.