Abstract: The annihilation of dark matter (DM) particles accumulated in the Sun could produce a flux of neutrinos, which is potentially detectable with neutrino detectors/telescopes and the DM elastic scattering cross section can be constrained. Although the process of DM capture in astrophysical objects like the Sun is commonly assumed to be due to interactions only with nucleons, there are scenarios in which tree-level DM couplings to quarks are absent, and even if loop-induced interactions with nucleons are allowed, scatterings off electrons could be the dominant capture mechanism. We consider this possibility and study in detail all the ingredients necessary to compute the neutrino production rates from DM annihilationsin the Sun (capture, annihilation and evaporation rates) for velocity-independent and isotropic, velocity-dependent and isotropic and momentum-dependent scattering cross sections for DM interactions with electrons and compare them with the results obtained for the case of interactions with nucleons. Moreover, we improve the usual calculations in a number of ways and provide analytical expressions in three appendices. Interestingly, we find that the evaporation mass in the case of interactions with electrons could be below the GeV range, depending on the high-velocity tail of the DM distribution in the Sun, which would open a new mass window for searching for this type of scenarios.