As disc galaxies form in a hierarchical cosmology, massive merging satellites are preferentially dragged towards the disc plane. The material accreted from these satellites forms a dark matter disc that contributes 0.25–1.5 times the non-rotating halo density at the solar position. Here, we show the importance of the dark disc for indirect dark matter detection in neutrino telescopes. Previous predictions of the neutrino flux from WIMP annihilation in the Earth and the Sun have assumed that Galactic dark matter is spherically distributed with a Gaussian velocity distribution, the standard halo model. Although the dark disc has a local density comparable to the dark halo, its higher phase space density at low velocities greatly enhances capture rates in the Sun and Earth. For typical dark disc properties, the resulting muon flux from the Earth is increased by three orders of magnitude over the SHM, while for the Sun the increase is an order of magnitude. This significantly increases the sensitivity of neutrino telescopes to fix or constrain parameters in WIMP models. The flux from the Earth is extremely sensitive to the detailed properties of the dark disc, while the flux from the Sun is more robust. The enhancement of the muon flux from the dark disc puts the search for WIMP annihilation in the Earth on the same level as the Sun for WIMP masses 100 GeV.