We report the controlled synthesis of AlN/GaN multi-quantum well (MQW) radial nanowire heterostructures by metal-organic chemical vapor deposition. The structure consists of a single-crystal GaN nanowire core and an epitaxially grown (AlN/GaN)(m) (m = 3, 13) MQW shell. Optical excitation of individual MQW nanowires yielded strong, blue-shifted photoluminescence in the range 340-360 nm, with respect to the GaN near band-edge emission at 368.8 nm. Cathodoluminescence analysis on the cross-sectional MQW nanowire samples showed that the blue-shifted ultraviolet luminescence originated from the GaN quantum wells, while the defect-associated yellow luminescence was emitted from the GaN core. Computational simulation provided a quantitative analysis of the mini-band energies in the AlN/GaN superlattices and suggested the observed blue-shifted emission corresponds to the interband transitions between the second subbands of GaN, as a result of quantum confinement and strain effect in these AlN/GaN MQW nanowire structures.