Dust grains in the interstellar medium and the outer Solar System commonly have a coating of water ice, which affects their optical properties and surface chemistry. The thickness of these icy mantles may be determined in part by the extent of photodesorption (photosputtering) by background ultraviolet radiation. But this process is poorly understood, with theoretical estimates of the photodesorption rate spanning several orders of magnitude. Here we report measurements of the absolute ultraviolet photodesorption yield of low-temperature water ice. Our results indicate that the rate of photodesorption is appreciable. In particular, it can account for the absence of icy mantles on grains in diffuse interstellar clouds, it exceeds solar-wind ion erosion and sublimation in the outer Solar System, and it is important in determining the lifetimes of icy mantles in dense molecular clouds.