Penitentes are snow and ice features formed by erosion that, on Earth, are characterized by bowl-shaped depressions several tens of centimetres across, whose edges grade into spires up to several metres tall. Penitentes have been suggested as an explanation for anomalous radar data on Europa, but until now no penitentes have been identified conclusively on planetary bodies other than Earth. Regular ridges with spacings of 3,000 to 5,000 metres and depths of about 500 metres with morphologies that resemble penitentes have been observed by the New Horizons spacecraft in the Tartarus Dorsa region of Pluto (220°-250° E, 0°-20° N). Here we report simulations, based upon a recent model representing conditions on Pluto, in which deepening penitentes reproduce both the tri-modal (north-south, east-west and northeast-southwest) orientation and the spacing of the ridges of this bladed terrain. At present, these penitentes deepen by approximately one centimetre per orbital cycle and grow only during periods of relatively high atmospheric pressure, suggesting a formation timescale of several tens of millions of years, consistent with crater ages. This timescale implies that the penitentes formed from initial topographic variations of no more than a few tens of metres, consistent with Pluto's youngest terrains.