Space missions and thermal infrared observations have shown that small asteroids (kilometre-sized or smaller) are covered by a layer of centimetre-sized or smaller particles, which constitute the regolith. Regolith generation has traditionally been attributed to the fall back of impact ejecta and by the break-up of boulders by micrometeoroid impact. Laboratory experiments and impact models, however, show that crater ejecta velocities are typically greater than several tens of centimetres per second, which corresponds to the gravitational escape velocity of kilometre-sized asteroids. Therefore, impact debris cannot be the main source of regolith on small asteroids. Here we report that thermal fatigue, a mechanism of rock weathering and fragmentation with no subsequent ejection, is the dominant process governing regolith generation on small asteroids. We find that thermal fragmentation induced by the diurnal temperature variations breaks up rocks larger than a few centimetres more quickly than do micrometeoroid impacts. Because thermal fragmentation is independent of asteroid size, this process can also contribute to regolith production on larger asteroids. Production of fresh regolith originating in thermal fatigue fragmentation may be an important process for the rejuvenation of the surfaces of near-Earth asteroids, and may explain the observed lack of low-perihelion, carbonaceous, near-Earth asteroids.