Recently, microelectromechanical system has been used to dynamically strain atomically thin materials including MoS2. While strain can significantly modulate the electronic and phonon structures of monolayer MoS2, its impact on electron transport, especially in the dissipative regime, has not been well explored. In this paper, using a three-dimensional particle-based quantum-corrected Monte Carlo device simulator, the effects of uniaxial and biaxial strain on room-temperature electron transport in a model monolayer molybdenum disulphide (MoS2) based field-effect transistor have been investigated. In the beginning, the simulator has been validated against recently published experimental results. Overall, strain in monolayer MoS2 strongly affects the polar optical phonon modes as well as the electronic bandstructure. Uniaxial strain breaks the degeneracy of E′ Raman mode and results in phonon softening. In this case, our results show that, for both E+ and E− Raman modes, ON current first increases for up to 3.7% of applied strain and then decreases as the strain is increased further. As for biaxial strain, we consider the effects of both tensile and compressive stresses. We find that the application of biaxial tensile strain boosts the ON current for up to 4% of strain. Especially, biaxial tensile strain leads to ~ 15.56% increase in the ON current, which is highest for any type of applied stress.