By applying the so-called Floquet engineering, we have done a detailed investigation and built a rigorous formalism for the electronic states of 1T'-MoS₂ in the presence of a linaarly polarized dressing field in the off-resonance regime. Our work includes both obtaining closed-form analytical expressions for the energy dispersions of the obtained dress states in some specific cases, such as an absence of the band gap for an initially non-irradiated material, and a thorough numerical investigation for all the other cases of the spin- and valley-polarized electronic band structure of 1T'-MoS₂. We have found that the effect of linearly polarized light on 1T'-MoS₂ is drastically different compared to that for any other known Dirac cone materials since the energy band gaps are also greatly modified by this type of  dressing field.