We investigate indirect neutrino signals from annihilations of Kaluza-Klein dark matter in the Sun. Especially, we examine a five- as well as a six-dimensional model, and allow for the possibility that boundary localized terms could affect the spectrum to give different lightest Kaluza-Klein particles, which could constitute the dark matter. The dark matter candidates that are interesting for the purpose of indirect detection of neutrinos are the first Kaluza-Klein mode of the U(1) gauge boson and the neutral component of the SU(2) gauge bosons. Using the DarkSUSY and WimpSim packages, we calculate muon fluxes at an Earth-based neutrino telescope, such as IceCube. For the five-dimensional model, the results that we obtained agree reasonably well with the results that have previously been presented in the literature, whereas for the six-dimensional model, we find that, at tree-level, the results are the same as for the five-dimensional model. Finally, if the first Kaluza-Klein mode of the U(1) gauge boson constitutes the dark matter, IceCube can constrain the parameter space. However, in the case that the neutral component of the SU(2) gauge bosons is the LKP, the signal is too weak to be observed.