The longitudinal magneto-optical conductivity of monolayer molybdenum disulfide (ML-MoS2) have 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 have two magneto-optical absorption peaks induced by the transitions processes within the conduction band in the 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 in visible to THz frequency range.