The nuclear-recoil correction to the bound-electron [Formula presented] factor in H-like atoms is calculated to first order in [Formula presented] and to all orders in [Formula presented]. The calculation is performed in the range [Formula presented]. A large contribution of terms of order [Formula presented] and higher is found. Even for hydrogen, the higher-order correction exceeds the [Formula presented] term, while for uranium it is above the leading [Formula presented] correction. As a result, one of the main sources of the theoretical uncertainty for the bound-electron [Formula presented] factor is eliminated.