The rate rivers erode their banks controls the pace of migration and the impacts on neighboring communities and ecosystems. Erosion of floodplains releases sediment, carbon, and other constituents into rivers affecting the biogeochemistry of rivers and ultimately the coastal oceans into which rivers flow.  Across the Arctic, rivers erode through floodplains frozen continuously for more than two years (permafrost). Before ice-bounded sediments can be eroded by flowing water they must be thawed. Using aerial photographs, satellite imagery, and direct field observations we found that permafrost slows the rate rivers erode their banks relative to rivers without permafrost. The effect of permafrost, however, varies with the size of the river, and the erosion rates of large rivers are disproportionately slowed by permafrost. As a result, permafrost thaw due to climate change will likely increase erosion rates on large rivers and have limited impact on small rivers, but very little data is available for small rivers in the Arctic highlighting a key data need.