Recently a new dark-matter candidate has been proposed as a consequence of universal compact extra dimensions. It was found that to account for cosmological observations, the masses of the first Kaluza-Klein (KK) modes (and thus the approximate size of the extra dimension) should be in the range 600-1200 GeV when the lightest Kaluza-Klein particle (LKP) corresponds to the hypercharge boson and in the range 1-1.8 TeV when it corresponds to a neutrino. In this paper, we compute the elastic scattering cross sections between KK dark matter and nuclei both when the LKP is a KK mode of a weak gauge boson, and when it is a neutrino. We include nuclear form factor effects which are important to take into account due to the large LKP masses favoured by estimates of the relic density. We present both differential and integrated rates for present and proposed germanium, NaI and xenon detectors. Observable rates at current detectors are typically less than one event per year, but the next generation of detectors can probe a significant fraction of the relevant parameter space.