We present the results of a low-energy neutrino search using the Borexino detector in coincidence with the gravitational wave (GW) events GW150914, GW151226 and GW170104. We searched for correlated neutrino events with energies greater than 250 keV within a time window of $pm500$ s centered around the GW detection time. A total of five candidates were found for all three GW150914, GW151226 and GW170104. This is consistent with the number of expected solar neutrino and background events. As a result, we have obtained the best current upper limits on the GW event neutrino fluence of all flavors ($ u_e, u_{mu}, u_{tau}$) in the energy range $(0.5 - 5.0)$ MeV.