We present the high-energy-neutrino follow-up observations of the first gravitational wave transient GW150914 observed by the Advanced LIGO detectors on September 14, 2015. We search for coincident neutrino candidates within the data recorded by the IceCube and Antares neutrino detectors. A possible joint detection could be used in targeted electromagnetic follow-up observations, given the significantly better angular resolution of neutrino events compared to gravitational waves. We find no neutrino candidates 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 were three and zero, respectively. This is consistent with the expected atmospheric background, and none of the neutrino candidates were directionally coincident with GW150914. We use this nondetection to constrain neutrino emission from the gravitational-wave event.