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, the quantum properties of an on-chip silicon nitride (SiN)-based magneto-optical (MO) isolator were studied using a single-photon non-reciprocal dynamical transmission experiment. The measured isolation ratio for single photons achieved was 12.33 dB, 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 isolators within the integrated quantum circuits and help introduce novel phenomena in quantum information processes.