A thick dark matter disk is predicted in cold dark matter simulations as the outcome of the interaction between accreted satellites and the stellar disk in Milky Way sized halos. We study the effects of a self-interacting thick dark disk on the energetic neutrino flux from the Sun. We find that for particle masses between 100 GeV and 1 TeV and dark matter annihilation to heavy leptons either the self-interaction may not be strong enough to solve the small scale structure motivation or a dark disk cannot be present in the Milky Way.