We have searched for exotic neutrino-electron interactions that could be produced by a neutrino millicharge, by a neutrino magnetic moment, or by dark photons using solar neutrinos in the XMASS-I liquid xenon detector. We observed no significant signals in 711 days of data. We obtain an upper limit for neutrino millicharge of 5.4×10−12e at 90% confidence level assuming all three species of neutrino have common millicharge. We also set flavor-dependent limits assuming the respective neutrino flavor is the only one carrying a millicharge, 7.3×10−12e for νe, 1.1×10−11e for νμ, and 1.1×10−11e for ντ. These limits are the most stringent yet obtained from direct measurements. We also obtain an upper limit for the neutrino magnetic moment of 1.8×10−10 Bohr magnetons. In addition, we obtain upper limits for the coupling constant of dark photons in the U(1)B−L model of 1.3×10−6 if the dark photon mass is 1×10−3 MeV/c2, and 8.8×10−5 if it is 10 MeV/c2.