Rocks dominated by the silicate minerals quartz and feldspar are abundant in Earth’s upper continental crust. Yet felsic rocks have not been widely identified on Mars, a planet that seems to lack plate tectonics and the associated magmatic processes that can produce evolved siliceous melts on Earth. If Mars once had a feldspar-rich crust that crystallized from an early magma ocean such as that on the Moon, erosion, sedimentation and volcanism have erased any clear surface evidence for widespread felsic materials. Here we report near-infrared spectral evidence from the Compact Reconnaissance Imaging Spectrometer for Mars onboard the Mars Reconnaissance Orbiter for felsic rocks in three geographically disparate locations on Mars. Spectral characteristics resemble those of feldspar-rich lunar anorthosites, but are accompanied by secondary alteration products (clay minerals). Thermodynamic phase equilibrium calculations demonstrate that fractional crystallization of magma compositionally similar to volcanic flows near one of the detection sites can yield residual melts with compositions consistent with our observations. In addition to an origin by significant magma evolution, the presence of felsic materials could also be explained by feldspar enrichment by fluvial weathering processes. Our finding of felsic materials in several locations on Mars suggests that similar observations by the Curiosity rover in Gale crater may be more widely applicable across the planet.