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The monolayer MoS₂ exhibits a strong optical response from the stable excitonic states even at room temperature, due to the large binding energy of the reduced dimension. We present that the topological chirality in MoS₂ binding the valleys and the spins determines not only the linear but also the nonlinear optical responses. Using the massive Dirac Hamiltonian to provide efficient handling of the nonlinear processes, we perform a perturbative calculation in the low-temperature and weakly excited limit. We then derive the linear and the nonlinear optical susceptibilities. We calculated those for particularly the second- and the third-harmonic generations, two-photon absorption, and optical Kerr effect, based on the prescribed optical selection rules. We compare the optical responses of the monolayer MoS₂ with our previous results on graphene, adopting the Keldysh-type wave functions and the S-matrix treatment. We also present the figure of merit for efficient optical Kerr device applications.