The polarization anisotropy of single GaN nanowires containing Al(x)Ga(1-x)N/GaN multiquantum disc (MQDisc) structures is characterized by polarization-resolved microphotoluminescence (mu PL). Single nanowires exhibit at T=4.2 K two main luminescence contributions: one is peaked at E=3.45-3.48 eV related to near-band-edge GaN bulk excitonic transitions and is polarized parallel to the nanowire axis (pi polarization) at moderate excitation-power density; the other, lying at higher energy, is related to excitonic transitions confined in the MQDisc and is polarized perpendicularly to the nanowire axis (sigma polarization). The results are interpreted in terms of the selection rules for excitonic transitions in wurtzite semiconductor crystals and of the polarization anisotropy arising from the elongated nanowire shape. Finally, the analysis of photoluminescence at T=300 K shows that the thermal population of light-hole states in the MQDisc produces a blueshift of the PL peak when polarization is rotated from sigma to pi.