Inspired by recent experiments for hybrid organic-ferromagnet interfaces, we propose a spin-relaxation mechanism which does not depend on either the spin-orbit or the hyperfine interaction. This takes place when a molecule with initial spin imbalance is weakly coupled to a metal surface and can be excited in various vibrational states. In such a situation the electron-vibron interaction promotes the exchange of spin-polarized electrons between the molecule and the surface, serving as an energy and angular momentum reservoir. This process leads to an effective spin relaxation of the electron population in the molecule. We suggest that this nonequilibrium mechanism can be investigated through time-resolved spin-polarized scanning tunneling microscopy experiments.