XMASS is a multi-purpose experiment using liquid xenon (LXe) and is located at the Kamioka Observatory in Japan. The detector consists is single-phase and has a 832 kg active volume, a low energy threshold, low background and large target mass. With XMASS, it is possible to also explore low energy neutrino physics to search for beyond teh standard model (SM) physics. Here we present a search for exotic neutrino-electron interactions that could be produced by a neutrino millicharge, a neutrino magnetic moment, or dark photons, using solar neutrinos. We analyzed data taken between November 2013 and March 2016, giving us a 711days dataset. No significant signal was observed above the predicted background in the detector. We thus obtained an upper limit for neutrino millicharge of $5.4\times10^{-11}$e for all flavors of neutrino. We also constrainted individual flavors to be smaller than $7.3 \times 10^{-12} e$ for $\nu_e$, $1.1 \times 10^{-11} e$ for $\nu_{\mu}$, and $1.1 \times 10^{-11} e$ for $\nu_{\tau}$. These limits for $\nu_{\mu}$ and $\nu_{\tau}$ are currently the best direct experimental limits. We also obtain an upper limit for the neutrino magnetic moment of 1.8$\times$10$^{-10} \mu_{B}$. In addition, we obtain upper limits for the coupling constant of dark photons in the $U(1)_{B-L}$ model of 1.3$\times$10$^{-6}$ if the dark photon mass is 1$\times 10^{-3}$ MeV$/c^{2}$, and 8.8$\times$10$^{-5}$ if it is 10 MeV$/c^{2}$. In particular, we almost exclude the possibility to understand the muon $g-2$ anomaly as originating from dark photons.