We present a search for a neutrino signal from dark matter self-annihilations in the Milky Way using the IceCube Neutrino Observatory (IceCube). In 1005 days of data we found no significant excess of neutrinos over the background of neutrinos produced in atmospheric air showers from cosmic ray interactions. We derive upper limits on the velocity averaged product of the dark matter self-annihilation cross section and the relative velocity of the dark matter particles Formula omitted. Upper limits are set for dark matter particle candidate masses ranging from 10 GeV up to 1 TeV while considering annihilation through multiple channels. This work sets the most stringent limit on a neutrino signal from dark matter with mass between 10 and 100 GeV, with a limit of Formula omitted for 100 GeV dark matter particles self-annihilating via Formula omitted to neutrinos (assuming the Navarro-Frenk-White dark matter halo profile).