We use nonequilibrium molecular dynamics modeling using Stillinger–Weber interatomic potential to investigate the thermal properties of monolayer molybdenum disulfide (MoS2) nanoribbons. We study the impact of factors such as length, edge chirality, monovacancies, and uniaxial stretching on the thermal conductivity of MoS2 nanoribbons. Our results show that longer ribbons have a higher thermal conductivity, and the thermal conductivity of infinitely long zigzag and armchair MoS2 nanoribbons is, respectively, 54 W/mK and 33 W/mK. This is significantly lower than the thermal conductivity of some other graphene-like two-dimensional materials such as graphene and boron nitride. While the presence of molybdenum or sulfur vacancies reduces the thermal conductivity of ribbons, molybdenum vacancies have a more deteriorating effect on thermal conductivities. We also have studied the impact of uniaxial stretching on the thermal conductivity of MoS2 nanoribbons. The results show that in contrast to three dimensional materials, thermal conductivity of MoS2 is fairly insensitive to stretching. We have used the phonon dispersion curves and group velocities to investigate the mechanism of this unexpected behavior. Our results show that tensile strain does not alter the phonon dispersion curves and hence the thermal conductivity does not change.