In the framework of a nonuniversal $U(1{)}^{\ensuremath{'}}$ extension of the standard model, we propose a scalar candidate for cold dark matter which exhibits interactions with ordinary matter through Higgs and gauge bosons. Using limits from low energy observables, we find constraints on the new physics parameters of the model associated to the extra Abelian symmetry, especially the mass of the additional neutral gauge boson ${Z}^{\ensuremath{'}}$ and the new gauge coupling constant. We find that for the lower experimental limit ${M}_{{Z}^{\ensuremath{'}}}=3\text{ }\text{ }\mathrm{TeV}$ constrained by direct research at LHC, the ratio between the $U(1{)}^{\ensuremath{'}}$ and $SU(2{)}_{L}$ gauge coupling constants is around 0.4. Taking into account this limit and the observable relic density of the Universe, we search for new constraints on the mass of the dark matter particle of the model. We find that for a Higgsphobic model, the mass of the scalar dark matter must be ${M}_{\ensuremath{\sigma}}=70\text{ }\mathrm{GeV}$. We also find different kinematical threshold and resonances that enhance the dispersion of dark matter into ordinary matter for different regions of the space of parameters of the model, obtaining masses as low as 1.3 GeV and as large as 125 GeV without allowed intermediate regions due to resonances.