We consider a dark matter scenario in the context of the minimal extension of the Standard Model (SM) with a $B-L$ (baryon number minus lepton number) gauge symmetry, where three right-handed neutrinos with a $B-L$ charge $-1$ and a $B-L$ Higgs field with a $B-L$ charge $+2$ are introduced to make the model anomaly-free and to break the $B-L$ gauge symmetry, respectively. The $B-L$ gauge symmetry breaking generates Majorana masses for the right-handed neutrinos. We introduce a $Z_2$ symmetry to the model and assign an odd parity only for one right-handed neutrino, and hence the $Z_2$-odd right-handed neutrino is stable and the unique dark matter candidate in the model. The so-called minimal seesaw works with the other two right-handed neutrinos and reproduces the current neutrino oscillation data. We consider the case that the dark matter particle communicates with the SM particles through the $B-L$ gauge boson ($Z_{B-L}^{\prime }$ boson) and obtain a lower bound on the $B-L$ gauge coupling (${\alpha }_{B-L}$) as a function of the $Z_{B-L}^{\prime }$ boson mass ($m_{Z^{\prime }}$) from the observed dark matter relic density. On the other hand, we interpret the recent LHC Run-2 results on the search for a $Z^{\prime }$ boson resonance to an upper bound on ${\alpha }_{B-L}$ as a function of $m_{Z^{\prime }}$. These two constraints are complementary for narrowing down an allowed parameter region for this “$Z^{\prime }$ portal” dark matter scenario, leading to a lower mass bound of $m_{Z^{\prime }}\ge 3.9$ TeV.