Riparian vegetation is part of one of the most diverse and fragile ecotones. The key role played by river discharge on the dynamics of riparian vegetation has been widely studied and documented. However, although randomness is a fundamental characteristic of river hydrology, very few quantitative vegetation studies take into account the random nature of river discharge. Here we propose a stochastic model of riparian vegetation ecosystem dynamics forced by random variations in river discharge. The model is solved, and the analytical expressions of the probability density function of the overall vegetation biomass and its first moments are obtained. These theoretical results are used to investigate the effect of river hydrology on the distribution of vegetation along the riparian transect transverse to the river. In particular, the influence of the type of riparian species and the statistical characteristics of discharge time series are discussed and compared with field observations.