Rivers in arid and semiarid regions often traverse saline aquifers, creating buoyant freshwater lenses in the adjoining riparian and floodplain zones. The occurrence of freshwater lenses where the river is otherwise gaining saline groundwater appears counterintuitive, given that both hydraulic and density forces act toward the river. In this paper, an analytical solution is presented that defines the extent of a stable, sharp-interface terrestrial freshwater lens (in cross section) in a riverine environment that otherwise contains saline groundwater moving toward the river. The method is analogous to the situation of an island freshwater lens, except in the riverine setting, the saltwater is mobile and the lens is assumed to be stagnant. The solution characterizes the primary controlling factors of riverine freshwater lenses, which are larger for situations involving lower hydraulic conductivities and rates of saltwater discharge to the river. Deeper aquifers, more transmissive riverbeds, and larger freshwater-saltwater density differences produce more extensive lenses. The analytical solution predicts the parameter combinations that preclude the occurrence of freshwater lenses. The utility of the solution as a screening method to predict the occurrence of terrestrial freshwater lenses is demonstrated by application to parameter ranges typical of the South Australian portion of the River Murray, where freshwater lenses occur in only a portion of the neighboring floodplains. Despite assumptions of equilibrium conditions and a sharp freshwater-saltwater interface, the solution for predicting the occurrence of riverine freshwater lenses presented in this study has immediate relevance to the management of floodplains in which freshwater lenses are integral to biophysical conditions.