Although many astrophysical and cosmological observations point towards the existence of Dark Matter (DM), the nature of the DM particle has not been clarified to date. In this paper, we investigate a minimal model with a vector DM (VDM) candidate. Within this model, we compute the cross section for the scattering of the VDM particle with a nucleon. We provide the next-to-leading order (NLO) cross section for the direct detection of the DM particle. Subsequently, we study the phenomenological implications of the NLO corrections, in particular with respect to the sensitivity of the direct detection DM experiments. We further investigate more theoretical questions such as the gauge dependence of the results and the remaining theoretical uncertainties due to the applied approximations.