We report the results of a neutrino search in Super-Kamiokande for coincident signals with the first detected gravitational wave 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 $sim$100 PeV, in a time window $pm$500 seconds 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 $16.0^{+0.7}_{-0.6}$ ($21.3^{+1.1}_{-0.8}$) cm$^{-2}$ for muon neutrinos (muon antineutrinos), with an error range of $pm5^{circ}$ 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 $6.6 times 10^7$ cm$^{-2}$ for anti-electron neutrinos under the assumption of a Fermi-Dirac spectrum with average energy of 20 MeV.
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