We report the observation of transverse-magnetic-polarized infrared absorption assigned to the s-p(z) intraband transition in Ge-doped GaN/AlN nanodisks (NDs) in self-assembled GaN nanowires (NWs). The s-p(z) absorption line experiences a blue shift with increasing ND Ge concentration and a red shift with increasing ND thickness. The experimental results in terms of interband and intraband spectroscopy are compared to theoretical calculations of the band diagram and electronic structure of GaN/AlN heterostructured NWs, accounting for their three-dimensional strain distribution and the presence of surface states. From the theoretical analysis, we conclude that the formation of an AlN shell during the heterostructure growth applies a uniaxial compressive strain which blue shifts the interband optical transitions but has little influence on the intraband transitions. The presence of surface states with density levels expected for m-GaN plane charge-deplete the base of the NWs but is insufficient to screen the polarization-induced internal electric field in the heterostructures. Simulations show that the free-carrier screening of the polarization-induced internal electric field in the NDs is critical to predicting the photoluminescence behavior. The intraband transitions, on the other hand, are blue-shifted due to many-body effects, namely, the exchange interaction and depolarization shift, which exceed the red shift induced by carrier screening.