The movement of fluvial sediment shapes our rivers. Understanding sediment entrainment has been a goal of hydraulic engineers for almost a century. Previous sediment entrainment models have been informed by laboratory experiments using grains that were free from biological material. In natural river settings, however, sediments are invariably covered by bacteria, often forming visible biofilms, which comprise diverse consortia of species housed in sticky extracellular polysaccharides. Here we report experiments in a laboratory flume with cyanobacteria grown over sediment. We show that the prevailing model, where grains roll over one another at some critical threshold in shear velocity, does not hold for biofilm-bound sediments. Instead, biostabilized sediment behaves more like an elastic membrane. Fluid flow produces oscillations in the membrane, which can become unstable. Beyond a particular threshold in velocity, the membrane fails catastrophically by ripping and clumps of biofilm-bound sediment become entrained. We use a mathematical model of an oscillating membrane in incompressible flow to show that unstable oscillations will occur over a wide range of elastic material properties at realistic river flow velocities. We find that the horizontal length scale over which oscillations occur is a controlling factor for incipient sediment entrainment of biostabilized sediments.