We constrain energy spectra of supernova neutrinos through the avoidance of an overproduction of the 11B abundance during Galactic chemical evolution. In supernova nucleosynthesis calculations with a parametrized neutrino spectrum as a function of temperature of nu(mu,tau) and nu(mu,tau) and total neutrino energy, we find a strong neutrino temperature dependence of the 11B yield. When the yield is combined with observed abundances, the acceptable range of the nu(mu,tau) and nu(mu,tau) temperature is found to be 4.8 to 6.6 MeV. Nonzero neutrino chemical potentials would reduce this temperature range by about 10% for a degeneracy parameter eta(nu) = mu(nu)/kT(nu) smaller than 3.