Although the nature of the early Martian climate is a matter of considerable debate, the presence of valley networks (VN) provides unambiguous evidence for the presence of liquid water on Mars’ surface. A subaerial fluvial origin of VN is at odds with the expected phase instability of near-surface water in the cold, dry Late Noachian climate. Furthermore, many observed geomorphometric properties of VN are inconsistent with surface water flow. Conversely, subglacial channels exhibit many of these characteristics and could have persisted beneath ice sheets even in a cold climate. Here we model basal melting beneath a Late Noachian Icy Highlands ice sheet and map subglacial hydrological flow paths to investigate the distribution and geomorphometry of subglacial channels. We show that subglacial processes produce enough melt water to carve Mars’ VN; that predicted channel distribution is consistent with observations; and corroborate geomorphometric measurements of VN consistent with subglacial formation mechanisms. We suggest that subglacial hydrology may have played a key role in the surface modification of Mars.