The Sombrero galaxy (NGC 4594) is an Sa galaxy with a symmetric dust ring. We have used the Large APEX BOlometer CAmera (LABOCA) at 870 mum and the MAx-Planck Millimeter BOlometer (MAMBO-2) at 1.2 mm to detect the dust ring for the first time at submillimetre and millimetre wavelengths. We have constructed a model of the galaxy to separate the active galactic nucleus (AGN) and dust ring components. The ring radius at both 870 mum and 1.2 mm agrees well with the radius determined from optical absorption and atomic gas studies. The spectral energy distribution of the ring is well fitted by a single grey-body with dust emissivity index beta=2 and a dust temperature T_d=18.4 K. The dust mass of the ring is found to be 1.6±0.2× 107 M_&sun; which, for a Galactic gas-to-dust ratio, implies a gas mass that is consistent with measurements from the literature. This publication is based on data acquired with the IRAM 30 m telescope and the Atacama Pathfinder Experiment (APEX). APEX is a collaboration between the Max-Planck-Institut fur Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory.