The halo dark matter (DM) can be captured by the Sun if its final velocity after the collision with a nucleus in the Sun is less than the escape velocity. We consider a selfinteracting dark matter (SIDM) model where U(1) gauge symmetry is introduced to account for the DM self-interaction. Such a model naturally leads to isospin violating DM-nucleon interaction, although isospin symmetric interaction is still allowed as a special case. We present the IceCube-PINGU 2σ sensitivity to the parameter range of the above model with 5 years of search for neutrino signature from DM annihilation in the Sun. This indirect detection complements the direct detection by probing those SIDM parameter ranges which are either the region for very small mχ or the region opened up due to isospin violations.