Bound states in the continuum (BICs) provide an alternative way of trapping light at nanoscale. Although the last 10 years have witnessed tremendous progress on BICs from fundamentals to applications, nonreciprocal BICs and their potential applications have not been fully exploited yet. In this study, we demonstrated a one-way quasi-BIC by leveraging an all-dielectric magneto-optical (MO) metasurface. We show that the key point for achieving a one-way quasi-BIC is to excite a magnetization-induced leaky resonance. Here we adopt the longitudinal toroidal dipole (TD) resonance characterized by a vortex distribution of head-to-tail magnetic dipoles parallel to the plane of the MO metasurface. We show that, by breaking the time-reversal symmetry, at critical conditions, the TD resonance can be enhanced in the forward channel and perfectly canceled in the time-reversed channel, resulting in a one-way quasi-BIC. The demonstrated phenomena hold significant promise for practical applications such as magnetic field optical sensing, nonreciprocal optical switching, isolation, and modulation.