We study the capture of WIMP dark matter by the Sun in the non-relativistic effective theory of dark matter self-interactions. The aim is to assess how self-interactions affect the expected neutrino flux coming from WIMP annihilation in the Sun, and to do so in a model independent manner. We consider all non-relativistic Galilean invariant selfinteraction operators that can arise from the exchange of a heavy particle of spin less than or equal to 1 for WIMPs of spin equal to 0, 1/ 2 and 1. We show that for interaction operators depending at most linearly on the momentum transfer, the WIMP-induced neutrino flux can be enhanced by several orders of magnitude compared to the same flux in absence of self-interactions. This is true even for standard values of the thermally averaged annihilation cross-section. This conclusion impacts the analysis of present and future observations performed at neutrino telescopes.