We report the first observation of the doubly-strange baryon $Xi(1620)^0$ in its decay to $Xi^-pi^+$ via $Xi_c^+ rightarrow Xi^- pi^+ pi^+$ decays based on a $980,{rm fb}^{-1}$ data sample collected with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. The mass and width are measured to be 1610.4 $pm$ 6.0 (stat) $^{+5.9}_{-3.5}$ (syst)~MeV$/c^2$ and 59.9 $pm$ 4.8 (stat) $^{+2.8}_{-3.0}$ (syst)~MeV, respectively. We obtain 4.0$sigma$ evidence of the $Xi(1690)^0$ with the same data sample. These results shed light on the structure of hyperon resonances with strangeness $S=-2$.