A river and its surrounding riparian vegetation are two dynamical systems that interact through several hydrological, geomorphological, and ecological processes. This work focuses on the role played by vegetation on meandering river morphodynamics: River planform evolution forces the riparian vegetation dynamics, which, in turn, affect the mechanical characteristics of the river banks and influence the meandering dynamics of the river itself. It follows that despite the fact that a traditional engineering approach considers vegetation as a static element the study of river morphodynamics should be coupled with the riparian vegetation evolution. To this end, a fluid dynamic model of meandering rivers is here coupled with a process-based model for the riparian biomass dynamics. The feedback of vegetation on river morphology is provided by a relation that links the biomass density to the bank erodibility. The numerical results highlight (1) the remarkable effects of the vegetation dynamics on meander evolution and (2) the role of the temporal scales of vegetation growth and decay in relation to typical morphodynamic scales. In particular, the differences with respect to the constant erodibility case can be of the order of tens or hundreds of meters (10--20% of the meander wavelength), and peculiar meander shapes that do not show the usual marked upstream skewness emerge.