The geometries, electronic structures, and magnetic properties of H-, B-, C-, N-, O-, and F-absorbed ${\text{MoS}}_2$ monolayers have been investigated by first-principles calculations. The results demonstrate that all these atoms can chemically absorb on ${\text{MoS}}_2$ monolayer. The total magnetic moments of H-, B-, C-, N-, and F-absorbed ${\text{MoS}}_2$ monolayers are 1.0, 1.0, 2.0, 1.0, and $1.0{\mu }_{\text{B}}$ , respectively. The large spatial extensions of spin density and long-range antiferromagnetic coupling were observed in H- and F-absorbed ${\text{MoS}}_2$ monolayers. Additionally, the $n$ -type and $p$ -type two-dimensional ${\text{MoS}}_2$ semiconductors can be realized by absorbing H and N atoms, respectively.