We present the high-energy-neutrino follow-up observations of the first gravitational wave transientGW150914 observed by the Advanced LIGO detectors on September 14, 2015. We search for coincidentneutrino candidates within the data recorded by the IceCube and ANTARES neutrino detectors. A possiblejoint detection could be used in targeted electromagnetic follow-up observations, given the significantlybetter angular resolution of neutrino events compared to gravitational waves. We find no neutrinocandidates in both temporal and spatial coincidence with the gravitational wave event.Within +-500 s of the gravitational wave event, the number of neutrino candidates detected by IceCube and ANTARES werethree and zero, respectively. This is consistent with the expected atmospheric background, and none of theneutrino candidates were directionally coincident with GW150914. We use this nondetection to constrainneutrino emission from the gravitational-wave event.