Radiative seesaw models have the attractive property of providing dark matter candidates in addition to generation of neutrino masses. Here we present a study of neutrino signals from the annihilation of dark matter particles which have been gravitationally captured in the Sun, in the framework of the scotogenic model. We compute expected event rates in the IceCube detector in its 86-string configuration. As fermionic dark matter does not accumulate in the Sun, we study the case of scalar dark matter, with a scan over the parameter space. Due to a naturally small mass splitting between the two neutral scalar components, inelastic scattering processes with nucleons can occur. We find that for small mass splittings, the model yields very high event rates. If a detailed analysis at IceCube can exclude these parameter points, our findings can be translated into a lower limit on one of the scalar couplings in the model. For larger mass splittings only the elastic case needs to be considered. We find that in this scenario the XENON1T limits exclude all points with sufficiently large event rates.