AlN/GaN heterostructures have been studied using density-functional pseudopotential calculations yielding the formation energies of metal vacancies under the influence of local interfacial strains, the associated charge distribution and the energies of vacancy-induced electronic states. Interfaces are built normal to the polar <0 0 0 1> direction of the wurtzite structure by joining two single crystals of AlN and GaN that are a few atomic layers thick; thus, periodic boundary conditions generate two distinct heterophase interfaces. We show that the formation energy of vacancies is a function of their distance from the interfaces: the vacancy-interface interaction is found repulsive or attractive, depending on the type of the interface. When the interaction is attractive, the vacancy formation energy decreases with increasing the associated electric charge, and hence the equilibrium vacancy concentration at the interface is greater. This finding can reveal the well-known morphological differences existing between the two types of investigated interfaces. Moreover, we found that the electric charge is strongly localized around the Ga vacancy, while in the case of Al vacancies is almost uniformly distributed throughout the AlN/GaN heterostructure. Crucially, for the applications of heterostructures, metal vacancies introduce deep states in the calculated bandgap at energy levels from 0.5 to 1 eV above the valence band maximum (VBM). It is, therefore, predicted that vacancies could initiate 'green luminescence' i.e. light emission in the energy range of 2.5 eV stemming from electronic transitions between these extra levels, and the conduction band, or energy levels, due to shallow donors.