Our theoretical findings demonstrate for the first time a possibility of band-gap engineering of monolayer MoS_2 crystals by oxygen and the presence of vacancies. Oxygen atoms are revealed to substitute sulfur ones, forming stable MoS_(2-x)O_x ternary compounds, or adsorb on top of the sulfur atoms. The substituting oxygen provides a decrease of the band gap from 1.86 to 1.64 eV and transforms the material from a direct-gap to an indirect-gap semiconductor. The surface adsorbed oxygen atoms decrease the band gap up to 0.98 eV depending on their location tending to the metallic character of the electron energy bands at a high concentration of the adsorbed atoms. Oxygen plasma processing is proposed as an effective technology for such band-gap modifications. Oxygen atoms are revealed to substitute sulfur atoms, forming stable MoS_ (2-x) O_x ternary compounds, or adsorb The top of the sulfur atoms. The substituting oxygen provides a decrease of the band gap from 1.86 to 1.64 eV and transforms the material from a direct-gap to an indirect-gap semiconductor. The surface adsorbed oxygen atoms decrease the band gap up to 0.98 eV depending on their location tending to the metallic character of the electron energy bands at a high concentration of the adsorbed atoms. Oxygen plasma processing is proposed as an effective technology for such band-gap modifications.