Since the discovery of the first exoplanets, it has been known that other planetary systems can look quite unlike our own. Until fairly recently, we have been able to probe only the upper range of the planet size distribution, and, since last year, to detect planets that are the size of Earth or somewhat smaller. Hitherto, no planets have been found that are smaller than those we see in the Solar System. Here we report a planet significantly smaller than Mercury. This tiny planet is the innermost of three that orbit the Sun-like host star, which we have designated Kepler-37. Owing to its extremely small size, similar to that of the Moon, and highly irradiated surface, the planet, Kepler-37b, is probably rocky with no atmosphere or water, similar to Mercury.