  We consider a hidden $U(1)$ gauge symmetry under which only the right-handed
neutrinos ($\nu_{R}$) are charged. The corresponding gauge boson is referred to
as the $\nu_{R}$-philic $Z'$. Despite the absence of direct gauge couplings to
ordinary matter at tree level, loop-induced couplings of the $\nu_{R}$-philic
$Z'$ via left-right neutrino mixing can be responsible for its experimental
accessibility. An important feature of the $\nu_{R}$-philic $Z'$ is that its
couplings to neutrinos are generally much larger than its couplings to charged
leptons and quarks, thus providing a particularly interesting scenario for
future neutrino experiments such as DUNE to probe. We consider two approaches
to probe the $\nu_{R}$-philic $Z'$ at DUNE near detectors via (i) searching for
$Z'$ decay signals, and (ii) precision measurement of elastic neutrino-electron
scattering mediated by the $Z'$ boson. We show that the former will have
sensitivity comparable to or better than previous beam dump experiments, while
the latter will improve current limits substantially for large neutrino
couplings.
