Non-reciprocal photonic devices are essential components of classical optical information processing. It is interesting and important to investigate their feasibility in the quantum world. In this work, a single-photon non-reciprocal dynamical transmission experiment was performed with an on-chip silicon nitride (SiN)-based magneto-optical (MO) isolator. The measured isolation ratio for single photons achieved was 12.33 dB, consistent with the result of classical test, which proved the functionality of our on-chip isolator. The quantum coherence of the passing single photons was further verified using high-visibility quantum interference. Our work will promote on-chip nonreciprocal photonic devices within the integrated quantum circuits and help introduce novel phenomena in quantum information processes.