Keeping the full quantum nature of the problem, we compute the relaxation time of the Holstein polaron in one dimension after it was driven far from the equilibrium by a strong oscillatory pulse. Just after the pulse, the polaron's kinetic energy increases and subsequently exhibits a relaxation-type decrease with simultaneous emission of phonons. In the weak coupling regime, partial tunneling of the electron from the polaron self-potential is observed. The inverse relaxation time is for small values of electron-phonon coupling λ linear with λ, while it deviates downwards from the linear regime at λ>/~0.1/ω(0). The imaginary part of the equilibrium self-energy shows good agreement with the inverse relaxation time obtained from nonequilibrium simulations.