In recent years III-nitride based nanowires have attracted a lot of interest because of their potential applications for nanoelectronic devices. Due to the large surface-to-volume ratio of the wires, the optoelectronic properties as well as growth processes are essentially dependent on the wire diameter. We have studied GaN NWs obtained by catalyst-free radio frequency PAMBE on Si(111) in N-rich conditions. Surface Photovoltage Spectroscopy and Spectral Photoconductivity (SPC) measurements have been carried out to analyze the near band-edge absorption in GaN nanowires. A strong diameter dependence of the band absorption tail was found by SPC measurements. The band-edge tailoring and its wire-diameter dependence can be explained by the Franz-Keldysh effect induced by the electric field at the wire surface. The experimental values of the absorption tail are well in agreement with the results obtained by simulating the electric field in a cylindrical model.