A search for dark matter (DM) particles produced in association with a hadronically decaying vector boson is performed using pp collision data at a centre-of-mass energy of √s = 13 TeV corresponding to an integrated luminosity of 36.1 fb −1 , recorded by the ATLAS detector at the Large Hadron Collider. This analysis improves on previous searches for processes with hadronic decays of W and Z bosons in association with large missing transverse momentum (mono- W/Z searches) due to the larger dataset and further optimization of the event selection and signal region definitions. In addition to the mono- W/Z search, the as yet unexplored hypothesis of a new vector boson Z ′ produced in association with dark matter is considered (mono- Z ′ search). No significant excess over the Standard Model prediction is observed. The results of the mono- W/Z search are interpreted in terms of limits on invisible Higgs boson decays into dark matter particles, constraints on the parameter space of the simplified vector-mediator model and generic upper limits on the visible cross sections for W/Z +DM production. The results of the mono- Z ′ search are shown in the framework of several simplified-model scenarios involving DM production in association with the Z ′ boson.