The longitudinal magneto-optical conductivity of monolayer molybdenum disulfide (ML-MoS₂) has been theoretically investigated under the quantizing Landau levels induced by applied magnetic field and proximity-induced exchange interaction via using the random-phase approximation (RPA) dielectric function approach. The effects of the proximity-induced exchange interaction and magnetic field on the longitudinal magneto-optical conductivity are examined. There are two magneto-optical absorption peaks induced by the transitions processes within the conduction band in Terahertz (THz) frequency range. The inter-band transitions between conduction and valence bands result in a series of magneto-optical absorption peaks in the visible frequency range. The results indicate that the magnetic field and proximity-induced exchange interaction could have important influence on the longitudinal magneto-optical conductivity of ML-MoS₂ and it could be applied in promising magneto-optics devices for spintronics and valleytronics working from visible to THz frequency range.