The first gravitational wave transient GW150914 was observed by Advanced LIGO on September 14th, 2015 at 09:50:45 Universal Time. In addition to follow-up electromagnetic observations, the detection of neutrinos will probe deeply and more on the nature of astrophysical sources, especially in the ultra-high energy regime. Neutrinos in the EeV energy range were searched in data collected at the surface detector of the Pierre Auger Observatory within ± 500 s and 1 day after the GW150914 event. No neutrino candidates were found. Based on this non-observation, we derive the first and only neutrino fluence upper limit at EeV energies for this event at 90% CL, and report constraints on existence of accretion disk around mergers.