Flows of water and sediment on Earth and other planets have a remarkable tendency to organize into channels across environments and scales. Channels are the primary conveyors of water, sediment, and nutrients through landscapes, and despite their prevalence, prediction of channel initiation and organization remains elusive. Models can predict channel initiation on steep hillslopes, but it is unclear how channelization arises on low-gradient floodplains. Here, we show that, in contrast to channelization on hillslopes, floodplains become channelized by headcutting at low specific discharges and moderate slopes (10−4 to 10−3 degrees). Using simplified numerical modeling of a floodplain with homogeneous soil, we show this difference arises because low specific discharge and moderate slopes maximize water drawdown at topographic discontinuities. Field data are consistent with model results and show that low specific discharges and moderate slopes are necessary, but not sufficient, conditions for channelization on floodplains in Indiana, Unites States. Our results imply that certain floodplains tend to self-channelize, and this increases the frequency of flooding and also enhances hydrological connectivity, which regulates biodiversity and nutrient processing.