The optical polarization properties of GaN/AlGaN core/shell nanowire (NW) heterostructures have been investigated using polarization resolved micro-photoluminescence (μ-PL) and interpreted in terms of a strain-dependent 6 × 6 k·p theoretical model. The NW heterostructures were fabricated in two steps: the Si-doped n-type c-axis GaN NW cores were grown by molecular beam epitaxy (MBE) and then epitaxially overgrown using halide vapor phase epitaxy (HVPE) to form Mg-doped AlGaN shells. The emission of the uncoated strain-free GaN NW core is found to be polarized perpendicular to the c-axis, while the GaN core compressively strained by the AlGaN shell exhibits a polarization parallel to the NW c-axis. The luminescence of the AlGaN shell is weakly polarized perpendicular to the c-axis due to the tensile axial strain in the shell.