A thin layer of fine‐grained sediment commonly is deposited at the sediment–water interface of streams and rivers during low‐flow conditions, and may hinder exchange at the sediment–water interface similar to that observed at many riverbank‐filtration (RBF) sites. Results from a numerical groundwater‐flow model indicate that a low‐permeability veneer reduces the contribution of river water to a pumping well in a riparian aquifer to various degrees, depending on simulated hydraulic gradients, hydrogeological properties, and pumping conditions. Seepage of river water is reduced by 5–10% when a 2‐cm thick, low‐permeability veneer is present on the bed surface. Increasing thickness of the low‐permeability layer to 0·1 m has little effect on distribution of seepage or percentage contribution from the river to the pumping well. A three‐orders‐of‐magnitude reduction in hydraulic conductivity of the veneer is required to reduce seepage from the river to the extent typically associated with clogging at RBF sites. This degree of reduction is much larger than field‐measured values that were on the order of a factor of 20–25. Over 90% of seepage occurs within 12 m of the shoreline closest to the pumping well for most simulations. Virtually no seepage occurs through the thalweg near the shoreline opposite the pumping well, although no low‐permeability sediment was simulated for the thalweg. These results are relevant to natural settings that favour formation of a substantial, low‐permeability sediment veneer, as well as central‐pivot irrigation systems, and municipal water supplies where river seepage is induced via pumping wells.