High-energy neutrinos (HEN) and gravitational waves (GW) can probe astrophysical sources in addition to electromagnetic observations. Multimessenger studies can reveal the nature of the sources, which may not be discerned from one type of signal alone. We discuss HEN emission in connection with the Advanced Laser Interferometer Gravitational-Wave Observatory event GW150914, which could be associated with a short gamma-ray burst detected by the Fermi Gamma-Ray Burst Monitor 0.4 s after the GW event and within localization uncertainty of the GW event. We calculate HEN flux from this short gamma-ray burst, GW150914-GBM, and show that nondetection of a high-energy starting event by the IceCube Neutrino Observatory can constrain the total isotropic-equivalent jet energy of this short burst to be less than 3×1052 erg. © 2016 American Physical Society.