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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 linear with , while it deviates downwards from the linear regime at . The imaginary part of the equilibrium self-energy shows good agreement with the inverse relaxation time obtained from nonequilibrium simulations.