First-principles study based on density functional theory has been employed to investigate width-dependent structural stability and magnetic properties of monolayer zigzag MoS2 nanoribbons (ZZ-MoS2 NRs). The width N = 4–6 (the numbers of zigzag Mo–S chains along the ribbon length) are considered. The results show that all studied ZZ-MoS2 NRs are less stable than two-dimensional MoS2 monolayer, exhibiting that a broader width ribbon behaves better structural stability and an inversely proportional relationship between the structural stability (or the ribbon with) and boundary S–Mo interaction. Electronic states imply that all ZZ-MoS2 NRs exhibit magnetic properties, regardless of their widths. Total magnetic moment increases with the increasing width N, which is mainly ascribed to the decreasing S–Mo interaction of the two zigzag edges. In order to confirm this reason, a uniaxial tension strain is applied to ZZ-MoS2 NRs. It has been found that, with the increasing tension strain, the bond length of boundary S–Mo increases, at the same time, the magnetic moment increases also. Our results suggest the rational applications of ZZ-MoS2 NRs in nanoelectronics and spintronics.