Theoretical analysis of nonadiabatic electron-transfer reactions in molecules usually assumes that electron amplitude propagates coherently from the reductant to the oxidant via covalent and noncovalent coupling pathways. We show that when the tunneling electron excites local bridge vibrations (inelastic tunneling), the excitation "labels" the physical pathway traversed. As such, the coherence among the bridge-mediated tunneling pathways is destroyed. We illustrate this effect using a simple model Hamiltonian and show how the donor-acceptor interaction, and thus the electron-transfer rate, is modified by inelastic effects. Pathway coherence loss provides a mechanism to relax orbital-symmetry constraints on electron-transfer reactions. This effect may be of particular significance in macromolecules with destructively interfering pathways or low tunneling barriers. Pathway decoherence that arises from inelastic effects in molecules is analogous to coherence loss in mesoscopic "which way" interferometers and might provide an approach to gate electron flow in molecular-scale devices.