Granites are nearly absent in the Solar System outside of Earth. Achieving granitic compositions in magmatic systems requires multi-stage melting and fractionation, which also increases the concentration of radiogenic elements1. Abundant water and plate tectonics facilitate these processes on Earth, aiding in remelting. Although these drivers are absent on the Moon, small granite samples have been found, but details of their origin and the scale of systems they represent are unknown2. Here we report microwave-wavelength measurements of an anomalously hot geothermal source that is best explained by the presence of an approximately 50-kilometre-diameter granitic system below the thorium-rich farside feature known as Compton–Belkovich. Passive microwave radiometry is sensitive to the integrated thermal gradient to several wavelengths depth. The 3–37-gigahertz antenna temperatures of the Chang’e-1 and Chang’e-2 microwave instruments allow us to measure a peak heat flux of about 180 milliwatts per square metre, which is about 20 times higher than that of the average lunar highlands3,4. The surprising magnitude and geographic extent of this feature imply an Earth-like, evolved granitic system larger than believed possible on the Moon, especially outside of the Procellarum region5. Furthermore, these methods are generalizable: similar uses of passive radiometric data could vastly expand our knowledge of geothermal processes on the Moon and other planetary bodies. Measurements from the Chang’e-1 and Chang’e-2 microwave instruments reveal an anomalously hot geothermal source on the Moon that is best explained by a roughly 50-kilometre-diameter granitic system below the geological feature known as Compton–Belkovich.