The new-type monolayer semiconductor material molybdenum disulfide (MoS2) is direct band gap semiconductor with a similar geometrical structure to graphene, and as it owns superior physical features such as spin/valley Hall effect, it should be more excellent than graphene from the viewpoint of device design and applications. The manipulation of the spin and valley transport in MoS2-based device has been an interesting subject in both experimental and theoretical researches. Experimentally, the photoninduced quantum spin and valley Hall effects may result in high on-off speed spin and/or valley switching based on MoS2. Theoretically, the off-resonant electromagnetic field induced Floquet effective energy should modulate effectively the electronic structure, spin/valley Hall conductance as well as the spin/valley polarization of the MoS2, through the virtual photon absorption and/or emission processes. Utilizing the low energy effective Hamilton model from the tight-binding approximation and Kubo linear response theorem, we theoretically investigate the electronic structure and spin/valley transport properties of the monolayer MoS2 under the irradiation of the off-resonant circularly polarized light in the present work. The band gaps around the K and K' point of the Brillouin region for monolayer MoS2 proves to increase linearly and decrease firstly and then increase, respectively with the increase of external off-resonant right-circularly polarized light induced effective coupling energy, and decrease firstly and then increase and increase linearly with the increase of left-circularly polarized light induced effective coupling energy, therefore, the interesting transition of semiconducting-semimetallic-semiconducting may be observable in monolayer MoS2. Furthermore, the spin and valley Hall conductance of the monolayer MoS2 for the case without off-resonant circularly polarized light are 0 and 2e2/h, respectively, and they will convert into -2e2/h and 0 when the absolute value of the off-resonant circularly polarized light induced effective coupling energy is in a range of 0.79-0.87 eV. Finally, the spin polarization for monolayer MoS2 increases up to a largest value and changes from positive to negative and/or negative to positive at the vicinity of the effective coupling energy ±0.79 eV of the off-resonant right/left circularly polarized light, while the valley polarization should increase firstly and then decrease with the off-resonant circularly polarized light, and goes up to 100% in the range of 0.79-0.87 eV of the absolute value for effective coupling energy. Therefore, the external off-resonant circularly polarized electromagnetic field should be an effective means in manipulating the electronic structure, spin/valley Hall conductance and spin/valley polarization of the monolayer MoS2, the two-dimensional MoS2 may be tuned into a brand bandgap material with excellent spin/valley and optoelectrical properties.