We report the results of a neutrino search in Super-Kamiokande (SK) for coincident signals with the first detected gravitational wave (GW) produced by a binary neutron-star merger, GW170817, which was followed by a short gamma-ray burst, GRB170817A, and a kilonova/macronova. We searched for coincident neutrino events in the range from 3.5 MeV to ~100 PeV, in a time window ±500 s around the gravitational wave detection time, as well as during a 14-day period after the detection. No significant neutrino signal was observed for either time window. We calculated 90% confidence level upper limits on the neutrino fluence for GW170817. From the upward-going-muon events in the energy region above 1.6 GeV, the neutrino fluence limit is ${16.0}_{-0.6}^{+0.7}$ (${21.3}_{-0.8}^{+1.1}$) cm−2 for muon neutrinos (muon antineutrinos), with an error range of ±5° around the zenith angle of NGC4993, and the energy spectrum is under the assumption of an index of −2. The fluence limit for neutrino energies less than 100 MeV, for which the emission mechanism would be different than for higher-energy neutrinos, is also calculated. It is 6.6 × 107 cm−2 for anti-electron neutrinos under the assumption of a Fermi–Dirac spectrum with average energy of 20 MeV.