  In this paper we show that the interaction between new light dark matter
mediators and the SM particles can be naturally suppressed if one employs a
single, flat extra dimension (ED). In this setup, the SM fields are localized
in a finite width `fat' brane, similar to models of Universal Extra Dimensions
(UED), while DM, in turn, is confined to a thin brane at the opposite end of
the ED interval. Including brane localized kinetic terms on the fat brane for
the mediator fields, the resulting coupling between the SM and these light
mediators can be several orders of magnitude smaller than the corresponding
ones between the mediators and DM which we assume to be a typical gauge
coupling. We investigate the implications of this scenario for both vector
(i.e., dark photon, DP) and scalar mediator fields in the 5-D bulk. In this
setup kinetic mixing, which is usually employed to suppress light mediator
couplings, is not required. Here we assume that the SM particles couple to the
DP via their $B-L$ charges while the DP couples to the DM via a dark charge.
Both the vector DP couplings and the corresponding Higgs portal couplings with
the SM are shown to be natural small in magnitude with a size dependent on
ratio of the 5-D compactification radius, $R^{-1} \sim 0.1-1$ GeV, and the SM
brane thickness, $L^{-1} \sim 2-10$ TeV, a range chosen to avoid LHC and other
experimental constraints. In this framework one can obtain the observed value
of the DM relic abundance for a wide range of parameter choices, while the
constrains due to direct DM detection and the invisible width of the Higgs do
not impose significant challenges to the model. Finally, this mechanism can
lead to distinct signatures in both present and upcoming experiments as it
combines some common features of UED and DP models in a single ED setup.
