Firn, an interannual layer made of a seasonal snow, covers the vast majority of the Greenland ice sheet. Firn holds the potential to buffer meltwater runoff by refreezing in its pore space. However, recent intensive summer melt and refreezing have led to the development of low-permeability ice slabs several metres thick in the shallow firn of the percolation zone, in areas that now often undergo visible surface runoff. Here, we analyse ice slab thickness retrievals from Operation IceBridge Accumulation Radar together with visible runoff limits derived from Landsat imagery. We constrain the minimum average ice slab thickness over spatial scales of kilometres that can support visible surface water flow as lying between 2.8 m and 3.5 m. We highlight that there is substantial heterogeneity in ice slab thickness, much of which can be explained by visible lateral meltwater flow over the slab and subsequent localised refreezing. Our findings provide a basis for improving how firn models partition between meltwater retention and runoff, by providing constraints on when simulated ice layers become impermeable enough to support lateral water flow over scales of several kilometres.