The extragalactic background light at far-infrared wavelengths(1-3) comes from optically faint, dusty, star-forming galaxies in the Universe with star formation rates of a few hundred solar masses per year(4). These faint, submillimetre galaxies are challenging to study individually because of the relatively poor spatial resolution of far-infrared telescopes(5,6). Instead, their average properties can be studied using statistics such as the angular power spectrum of the background intensity variations(7-10). A previous attempt(11) at measuring this power spectrum resulted in the suggestion that the clustering amplitude is below the level computed with a simple ansatz based on a halo model(12). Here we report excess clustering over the linear prediction at arcminute angular scales in the power spectrum of brightness fluctuations at 250, 350 and 500 mu m. From this excess, we find that submillimetre galaxies are located in dark matter haloes with a minimum mass, M-min, such that log(10)[M-min/M-circle dot] = 11.5(-0.2)(+0.7) at 350 mu m, where M-circle dot is the solar mass. This minimum dark matter halo mass corresponds to the most efficient mass scale for star formation in the Universe(13), and is lower than that predicted by semi-analytical models for galaxy formation(14).