The valley degree of freedom and the possibility of spin-valley coupling of solid materials have attracted growing interest, and the relaxation dynamics of spin- and valley-polarized states has become an important focus of recent studies. In spin-orbit-coupled inversion-asymmetric two-dimensional materials, such as MoS_{2} it has been found that the spin randomization is characteristically faster than the time scales for inter- and intra-valley scatterings. In this study, we examined the ultrafast non-collinear spin dynamics of an electron valley in monolayer MoS_{2} by using real-time propagation time-dependent density functional theory. We found that the spin precession of an electron in the valley is sharply coupled with the lowest-lying optical phonon that release the in-plane mirror symmetry. This indicates that the spin randomization of MoS_{2} is mainly caused by spin-phonon interaction. We further suggest that flipping of spins in a spin-orbit-coupled system can be achieved by the control over phonons.