We investigated the polarization dependence of the near-band-edge photoluminescence in ZnO strain-free nanowires grown by vapor phase technique. The emission is polarized perpendicular to the nanowire axis with a large polarization ratio (as high as 0.84 at 4.2 K and 0.63 at 300 K). The observed polarization ratio is explained in terms of selection rules for excitonic transitions derived from the k·p theory for ZnO. The temperature dependence of the polarization ratio evidences a gradual activation of the X C excitonic transition. PACS: 78.55.Cr, 77.22.Ej, 81.07.Gf.