Internally drained catchments (IDCs) are hydrologic units on the Greenland Ice Sheet (GrIS) surface that collect and drain meltwater through supraglacial stream/river networks to terminal moulins or lakes. Their areas and shapes constrain the volumes and locations of supraglacial meltwater penetration into the ice. We map IDCs of the southwest GrIS by using Landsat‐8 Operational Land Imager panchromatic imagery and a moderate‐resolution digital elevation model (DEM). In total 919 IDCs are mapped between 400 m and 2000 m above sea level, together with their associated supraglacial river networks (total length of 21,129 km), supraglacial lakes (436), and terminal moulins (872). A complex yet broadly predictable surface drainage pattern is revealed, with both IDC areas (AIDC, averaging 17.0 ± 22.8 km2, range of 0.4–244.9 km2) and the optimal DEM depression‐filling threshold (Adep, varying from 0.2 to 1.0 km2) generally increasing with ice surface elevation H. Historical air photos suggest possible transferability of the first relationship over space and time. Intersection of IDC boundaries with Modèle Atmosphérique Régional regional climate model runoff simulations shows >50% of runoff modeled for elevations >1600 m is not transported downstream to lower elevations, but instead drains to a small number (51 out of 872) of terminal moulins, indicating modest but nontrivial penetration of surface meltwater at high elevations. In sum, IDCs provide a new, fine‐scale hydrologic unit for study of GrIS surface hydrologic processes.