  In models with one universal extra dimension (UED), the first Kaluza-Klein
excitations of the hypercharge gauge boson, B^(1), and the neutral component of
isospin gauge boson, W^3(1), are each viable dark matter candidates. In either
case, such particles are predicted to accumulate in the core of the Sun, where
they annihilate to generate a potentially observable flux of high energy
neutrinos. In this article, we calculate the flux of neutrinos produced in this
model and determine the constraints that can be placed on the UED parameter
space from current IceCube data. For the case of B^(1) dark matter, we find
that the present limits from IceCube are stronger than those from direct dark
matter detection experiments such as CDMS and XENON10. For W^3(1) dark matter,
the present IceCube data provides a constraint slightly weaker than direct
detection experiments. In addition, we also present the projected regions of
UED parameter space that can be probed by IceCube/DeepCore in the near future
and compare them to the prospects for future direct detection experiments.
